Hello everyone good evening and welcome to today's class so i hope that everyone is in good health please just give a confirmation that audio video everything is clear good evening lexina good evening okay thank you good evening aisha .

Good evening reika okay so yesterday uh we had done 13 questions we we did certain questions on proposition logic and few more questions are there okay a few more concepts basically uh good evening preeta good evening so today we will be discussing those concepts .

Basically i hope you have heard rules of inferences there tickets on basis of those we have certain questions and uh rest okay so this is the propositional logic part two we are doing like this practice questions we are practicing certain questions and this is the telegram channel that you can join .

Net urea digimento ck so here we try to provide the pdf of all the lectures that i take and moreover other you are also know informed about other classes that are being going on that that will take place and plus without solving sessions is always available to everyone okay .

So without wasting any more time these questions we have already done so let's start with today's class so okay so uh this is the today's class this is today's first question is it visible everyone question is visible to everyone good evening good evening harshita good evening kitty so .

This is the first question i hope this is visible to everyone okay so they have given you four statements p q r and s good evening tripty good evening nandini and they are saying that they have given you four statements and they are asking that which of the following uh .

Arguments that this pqrs arguments are valid good evening mary lakshmi okay so basically you have you are given pqrs small pqrs as for primitive statements and then you have been given four arguments capital pqrs and they are asking out of these four arguments which of the following are .

Valid okay good evening so try everyone try this question um i'm just trying to zoom out zoom in which is okay so um this is the statement here they have .

Negation s implies q okay negation s implies q here first uh if it is visible to you then you can do this one and then i'll show you the statement okay good evening teach come tech good evening good evening radhika hello so these are the statements these are four statements arguments basically pqrs .

Ticket if this is okay basically they are asking which of the following arguments are valid you good evening sara banan good evening yes so what is everyone getting in the answer d okay see whenever you have questions of these .

Type ticket uh let us see the correct answer the correct answer is option number c okay so whenever you have questions of this type that is that if you see that there are certain uh type of arguments are there tk certain type of propositions are there and they are .

Connected with the help of what they are connected with the help of this and okay so whenever you have this type of thing what you have to do always and then they are in they are then implied this if this is the type okay a implies b this is the type and this a is basically composed of so many .

Uh what you can say propositions that are connected with the help of or and all together they are connected with the help of and if this is the type okay if this is the type good evening just now so always always use rules of inference rule of inference .

That is your resolution okay so always use that rule that is resolution principle so what is resolution build principle basically it says that these uh these are terms as premises okay what we can say they can be termed as your premises or they can be termed as your clauses .

Okay so when these premises or these clauses that are basically disjunction so i hope everybody knows that this that is your or is basically known as disjunction right i hope this you everyone knows that this is your disjunction and this that refers to end is what is .

Your conjunction right good evening gaurav okay so whenever you have this type of statement that you are having what you can say you are having basically the disjunctions or you can say these disjunctions are they are connected with .

The help of what they are connected with your uh and operator okay they are connected with and operator then you can use this resolution now basically what is this resolution now if we see here right so if we just look um i think you all have started doing that .

What you say now um put a simplified kind of but there is no need of simplifying ticket what you can do is simply best method is up subsequently you took your p to get pj bob neal here so p is what p is basically negation of if i'll do here only .

So we have p so first we will take negation of p or q okay so this is here this is your first premise this is your first premise then we have and then we have second premise that is our implies s then we have this is the second premise and this is the third one so this is .

Your second one and this is your third premise or clause anything you can say like this okay now what you have to do now you have to convert this r implies s in your disjunction form so what it will be it will be negation r or s right this is what you will get this .

Much is clear everyone okay so what now what i have to do now i will perform the resolution now what does resolution says it says that when you have this type of statements when they are in disjunction form and they are connected to each other with the help of conjunction .

So what you have to do good evening heather so what you have to do you have to cancel out those terms that are complement of each other okay good evening rosalind i'll explain you what i'm trying to say suppose i have this thing that is p or q and negation p or q if this is my proposition ticket this is .

The proposition and they are asking it implies to what if this is the question that they're saying that this p or q and negation p or q implies to what so what you will do you will apply this resolution why you will apply resolution because you will see that they .

Are these premises are your disjunction this junction means they are connected with the help of this or and between them they are connected with this and symbol so how you will write you will write first premise just a logical reasoning if you remember we write no this is the premise this is the second premise and then we .

Draw the conclusion so here we will draw the conclusion now how we draw the conclusion we'll draw the conclusion with the help of this that is p and complement of p they are complement of each other so they will cancel out each other so this p and its complement will cancel out each other .

Q and q will give only q so the result of this proposition is small q so why we're using this method in order to save time now if this is very simple state this is by simple proposition you can even solve it by opening this bracket but what will happen this is a small example i'm saying .

But if your question is big as we have in this case so it will take a lot of time for us to solve this entire question so we will apply this method so now we are taking this p argument okay let us talk about this p only now if you will try to see here you try to cancel out .

So negation p and this p will cancel out each other then we have negation r and r so negation r and r will cancel out each other what we have we have we have s or q okay we have this only so i can write it as s or q or i can write it as q or s .

Whatever you want to write you can write it like this take it so now if you try to resolve this if you try to simplify this part what it will be negation s implies q will become negation of negation s or q so what it will be it will be s or q so this term and this term they .

Both are equal so i can say that yes they are equal that is they are valid getting my point everyone since the result that is if this is my a and this is my b so i have to find that whenever i will solve this part it should imply to this .

So when this and this are equal so i will say that my argument p is valid any doubt in this one okay so now p is valid now we'll see the options best thing best thing is thus try for the elimination now p is in every statement so i cannot cancel out ptk now .

Let's check for q next we will check for your statement that is your argument q so now we will check for good evening victory ace good evening okay now let's check for the argument q so what is q q is negation p and q okay so and again so this is a different statement .

And now we have this thing now we will open this first so what it will be if i have to open this it is q implies p implies r okay so first we will open p implies r it will be negation p or r and then i have to this so it will be q negation .

Q or negation p or r right so what i will write i will write here negation q or negation p or r this is what i will get tk now i will try to solve it what it will become i try to cancel out the terms that are canceling that are complement of each other so negation piece and negation p .

Cancel over here q say negation q cancel remaining ayah after r but if you see here final may they have given you complement of r if you see this statement this is saying complement of r and what we are getting we are getting only r right so this .

Means that this is not valid right so this and this is not valid so i will simply write not valid so this means that q is not valid so i'll check the options that are sink u so a will cancel out and d will cancel out this much is clear basically yahape they must they just .

Forgot i think they should have put a bracket over here because like this it will be like this why because whenever you will have this conjunction no this is basically treated as a different premise okay so this is what this is the easiest way negation pc negation p oh okay okay okay .

Okay okay right right sorry sorry sorry right so negation p will remain as it is right correct so this will be negation p or r correct ticket so negation p or r is not equal to negation r as mentioned in the question clear okay everyone now let's check for option number r .

Let's check for r so i have this r what is the argument r argument r is negation what is the argument r and q uh q are infinite q r implies p so i'll do it here let's so what is our r is basically q and r okay so first we will open this .

One so it is q and r implies p so first let us open this thing so it will become what negation of q and r or p right so what it will be it will be negation of q or negation of r or p this is your first reminds when you will solve this premise .

And we have negation of q or p now try to cancel out so what will cancel nothing will cancel out each other because there is no proposition that are uh what you can say complement of each other p p complement q complement q r so it will be p or negation q or r and this .

Is not equal to r so this is also invalid so p is valid so we will cancel out what we will cancel out r as well so b will also cancel out and c will only remain right y r is not valid see r is not valid this our argument .

We're talking the whole r argument see what you have to do you have to first open the brackets one by one tk so this is the first whole bracket so what you will do you will open it so when you will open it what you will get you will write you will get that this is q .

And r implies p okay so what you did you open this bracket you will get this thing you will get this thing when you will open the first premise that is your this one and we have and so as soon as we'll see and we will write it in the next line that is the next premise okay then we have negation q .

Or p so we will write it like this and we will we see what are complementing each other and we will cancel out those terms but here in this r part nothing is complementing each other so we will have to write them as it is and in result they are saying that result should be equal to r which is not .

The case we try s everyone try for this s part let's see this s also so p and so p hat p this is written over here first we will solve this p implies r it will be negation p or r and we have q or negation r so q or negation r now we will solve it so what will happen .

P say p will cancel because this is p this is negation p r and r negation will cancel and result will be q so here we are having q that is this is valid so this means that p and s are only valid terms rest all are invalid okay so this is why uh i have told this why i have .

Introduced this question basically because this will solve a lot of time white will save a lot of time because must have known p and s are equal yes valid so equally correct many of you must have not known this method so you would have solved this question by simplifying it .

Right so it would have taken a lot of time so that is why this is the easiest method to solve these type of questions tk this is basically your rules uh resolution principle now next question next is consider the following statements they have given you two statements s one and s two tick em .

Then they are saying negation p is tautologically implied by this proposition and statement 2 is saying negation p is tautologically implied by this proposition so they are asking which of the following is true and false i'll just uh okay .

First up uh this is your statement one if you if it is not visible to you i have uh zoomed it so you can please just copy it once so they are saying negation of p is tautologically implied by then you have this statement you can just copy this everyone .

Just copy problem warrior statement just could be blurred screen please i think if you will change your quality know quality of video i think up visible or clear if you're not able to if it's not clearly visible please change the quality once of your video okay so this is one proposition they are giving they have given a set of .

Propositions and they are saying that this negation piece tautologically implied by this and then statement 2 is saying same thing but the set of propositions are different okay so try this once um .

In this resolution know one thing you have to keep in mind that uh yaha pay joby uh propositions that you are taking as premises they all must always be having an or that is this junction ticket that is very important always keep this thing in mind whenever you will apply this resolution method .

Always keep this in mind that the literals that you are taking the premises that you are taking clauses basically they must be connected with this or operator with each other and with these two premises must be connected with and okay good evening jyoti done .

Okay okay hello let's see the correct answer is option number c both s1 and s2 are true now how see try to understand this statement they are saying that negation p is tautologically implied by so they are trying to say .

With statement one what they are trying to say that this whole your negation p and negation q and negation q or r and negation r basically they are saying that this all is tautologically implied by this means that when you will solve this part .

You will get this that is both of them are true that is both of them are valid tautologically implied means they are always true so best what you can do just apply the resolution without looking anything now many of you will think that this is .

Uh this is what you can say um comma how can we convert it into and so basically whenever they say implied whenever implied means see whenever you will see this word logically implied okay so logically implied basically means that they are talking .

If a then b so if they are saying tautologically implied they are direct indirectly saying that if you have these propositions so these propositions will tautologically imply negation p so here when you will convert it into this a .

And if for this this form that is your implication form they will automatically change to and okay so now let us try to solve this so what you will get if i talk if i take this s1 let's see this s1 so we have if we look at this premise they have negation outside and then they .

Have p and negation q so what you will get if you will solve this you will get negation p or because and will convert to r and you will get q then we have negation q or r and we have negation r now try to solve this now we will try to .

See what is cancelling out each other so negation p is nothing q say negation q will cancel out r say negation r will cancel out so result will come out to be negation p and what they are saying here also they are talking about negation p only so this means that this is equal to this so .

S1 is correct now let's check for s2 same thing in s2 now what will happen in s2 if you look here estimate they are first they have implied they have used this implication so you will change this implication what it will become it will become i'll write here s2 it will become negation r .

Or negation q then we have r or s so we'll simply write r or s then we have s implies negation q so in negation s or negation q and then we have p implies q so negation p or negation sorry negation p or q only okay now when you will try to solve this what you will get .

Negation r and r will cancel out each other then s and negation s will cancel out each other and we have two times negation q so it will be treated as one negation key only and they will cancel out with this q so result only negation p and this is what they .

Are saying that negation p is tautologically implied by this thing so we are getting negation p only so this means s2 is also valid so that is both s1 and s2 are true that is negation p is tautologically implied by this propositions and negation beats are .

Logically implied by these propositions so both s1 and s2 are correct clear any doubt in this question okay now moving on to the next question now they are saying the notation this symbol to get this symbol denotes implication that is implies .

And this symbol denotes and okay so basically they are telling you the basic meanings of the symbols and they have given you two propositions or two formulae x and y so x is basically this i'll write uh if you want i can zoom in so x is basically .

B implies a implies a implies b and y is basically a implies b and b so they are asking which of the following is true out of these five options which of the following option is true so yesterday only we have discussed satisfiable and tautology so i hope you all remember .

That okay so try to do this and tell me what will be the answer according to you i think it's okay so i have tried to cover each and every important question that we can have for your proposition logic only for proposition i'm not talking about predicate one only proposition .

So if you will practice any more questions i think you will be able to do the questions now because i have tried to cover each and every concept that is possible for your net point of view okay um yes um lately many of you have been asking about the important topics .

Of exam right like what are the main topics that you have to focus what are the less important topics we have to focus so i was thinking of uh making an analysis class type of analysis class from the 2020 paper we'll try to see what are the important topics that have been .

Asked and what are the new questions that have been introduced in 2020 paper and regarding the entire syllabus what are the important important uh topics i was thinking of uh having a class like this so i just wanted to know that uh you do you want that type of class or .

No i said though i think it will be good to have that type of class just a type of what you can say um analysis class both important parts important topics both people do i'm thinking of putting a session like this so do give your views that what you want and .

Yes done everyone okay so the correct answer is option number d now why option number d is the correct answer if you look here let us look at your uh formula x okay let us look at x1 what they are saying they are saying that b implies a .

Implies a implies b right this is what they're saying so we solve it b implies a basically is negation b or a then we have negation implication over here and then we have a implies b so this will be this thing now we will solve this one implication so it will be negation negation b or a or negation .

A or b right so what we have to do this will become b this will become and and this will become negation a then this will become or this will become negation a or b so when you will saw open it you can change this good evening additi no problem so this .

Will become b a complement plus a complement plus b right so when you will solve these two you will get b plus a complement this is what you will get right now when i'm seeing this thing i can say that i will not get every time a true .

Value right this i can say for sure why because if my b is if my b is true or if i say that my b is false okay if my b is false and a is true okay b is false and a is true so what will be the value of this thing .

It will become it will turn out to be b is false plus true complement is false so i will get false but there will be certain cases when i will get true as well okay so this means that this x is basically what this x is satisfiable .

But not tautology okay so x2 i am i know this x is satisfiable so x is satisfiable x is satisfiable x is not tautology x is not logic correct but this e is wrong that is x is a total logic okay now let's check for y now if i apply the same procedure for y .

What it what i will get i will get a negative a implies b will give me negation of a or b right and it will give me and b so now what it will happen is a complement plus b multiply by b so this will be what it will be .

A complement b plus b and it will give you a simple b only when you are simplified okay many of you what you will do is so you will just keep it this way like this only no if you will mult you are removing this sign you have to multiply it with .

The entire bracket put it back in multiply so this will give you b now what will happen is now b can either be true and it can either be false so definitely this will also not be a tautology but it will be satisfiable so the correct answer will turn out to be option number .

D any doubt in this part any doubt in this question anyone okay so i think you know what is your mistake where you made the mistake okay now i have a question okay i have a question i just want everybody should tell me what it will give so there is one .

Statement first statement is that if it rains i don't know whether i have discussed this okay uh victory is okay just wait let me just give this question then i'll then explain to you the concept okay so if it trains then i'll tell you this also uh okay i'll .

Tell you okay by a question just let me write this question once then cricket match will not be played so this is your first statement and a second statement is cricket match was played so the conclusion that was drawn from it .

Is there was no rain now you have to tell whether it is valid or not okay so before moving uh before moving here let me just clear everyone's doubt okay what is the doubt gaurav is saying no my new concept okay okay thank you god of .

So much yes victory is you are saying uh satisfiable see satisfiable basically means that at least one when you are having a truth if you make a truth table and this is your final result so in this final result at least .

One value at least one value must be true okay at least one value must be true that is your satisfiable and when you have valid valid says when you are talking in terms of valid valid says that all the values must be true if this is your final thing so valid is equivalent to tautology .

And satisfiable is equivalent to contingency okay okay and then radhika was saying ma'am if we have done where truth table means how to find satisfiable if this was the question if i take this thing that is b plus a complement okay so what you have to do nothing you can just simply what you do .

You have this a plus b complement make a truth first up school simplify color for a statement go first simplify the entire statement and then you this is the result you are getting now what you do draw the truth table this is a this is a complement to b complement i think it is it is a complement b it is .

Not a b complement it is it is a complement plus b so draw the truth table first so this will be true true true false false true and false false now we have what we have a complement plus b sorry so what we do we will write a complement so what is a complement now .

A complement is this is false this is false this is true and this is true right then we have a complement plus b so now perform the or between these two so when you will do it it will become this will come out to be true this will turn out to be false this will turn out to be true this will turn out .

To be true so we have at least one value as true so when we have at least one value as true we will say that this is satisfiable and if all the values would have been true we would have said this is a tautology okay okay so what are you saying everyone they are saying valid .

Not valid valid valid valid okay so yeah now let's look here what you have to do how you have to do first just write it as if it rains rains while a part go we will say how you will solve this let's say it rains go we are denoting with r okay and we are saying cricket match will be played played .

Cricket played so we are denoting with capital p now if i have first statement okay this is the first statement what will be the propositional representation of first statement it will be if it rains that is this thing if it rains then cricket match will not be played .

This is my first statement second is saying cricket match was played this is your second thing and then you have to find this conclusion so you can write this statement as negation of r or negation of p okay now what you have to do now you can cancel out the term so negation of p .

And p will cancel out so result will turn out to be negation of r and it is this negation of star mean that there was no rain and conclusion is also there was no raid so this means that this is valid tk now um okay so you have taken three terms .

Complicated okay now let's have uh one more question let me give you one more question yes correct let me give one more uh the question is statement one is if a candidate is corrupt he will not be elected he will not .

Be elected and statement two is if a candidate is kind he will be elected so you have to find you have to tell what will be the conclusion of this statement what will be the conclusion of these statements .

How p canceled p cancel because we were having p and negation p so when you have a term and its complemented term also so they will cancel out each other try this one and tell me what is the conclusion that you are getting so what you can do i'll just help you a little bit what you can do here is .

Candidate is corrupt so let for c you can say corrupt candidate you can write elected and with k you can denote kind so with the help of these three variables i think you can solve this proposition and you can tell me what will be the conclusion okay hmm .

Correct heather correct it is so let's look here everyone see not not so let's see let us see what will be the first premise first premise will become if a candidate is corrupt that is this is the candidate it is corrupt then he will not be elected that is this .

Statement okay then second is basically what they are saying if the candidate is kind then he will be elected right so now what we have to do we have to solve this so what will be the first statement the first statement will become what it will be uh negation of c or negation of e and second is negation .

Of k or e this is the statements right so this and this will cancel out because this is negation and this is not negation so this is negation of c or negation of k so this means that you can say if the candidate is not corrupt .

There are two ways of writing this either you can write it like this or you can write it like this so this means that if a candidate is corrupt then he is not kind and if a candidate is not kind then he is corrupt we have to connect these two propositions then we will apply this and .

Okay i have one more question that is on basically uh key satisfiability and validity so there's one more just this is the last of today's class um so the question is p implies q or r .

Implies p and q implies r this is the statement okay i hope this is visible to everyone and they are saying that you have to tell whether this proposition is satisfiable or valid what it is according to you .

So this you have to see how you will solve this and how you will do it and tell me whether it is satisfiable or valid or total logic logic is so valid right so satisfiable of valid what you think according to you it is best thing is after simplifying now change this or and and to plus and .

Multiplication so but simplify about easy check in order to solve this valid okay so let's see so done everyone let's start okay everybody is getting valid only so now let's start solving this so first we'll solve this thing so it will become .

Negation of p this will become or this is q or r right this is your this thing implies then we have what we have p negation of p and q or r i just and it is same optimism .

Actually you have applied that resolution method okay shallow resolution method let's let's see so the first let's apply the resolution method only so they are asking satisfiable or valid you happy they are not asking .

Whether this statement is logically implied or not you have to see this thing okay johan questions we were doing they were asking you whether these statements were valid or not that is correct but now they're asking whether they're satisfiable or valid okay so when you're having this type of .

Things that is satisfiable or valid and they're not talking about logically implied or when they're not talking about implication thing then in that case you have to simplify it why am saying this if you see like this if you see here this will become negation this will become whole .

Complement so it will become negation p plus q plus r oh sorry basically you have to tell whether it is satisfiable or not satisfiable of validity valid getting my point everyone valid they were talking about valid that was basically term and diwali term ecologically .

Implied hori thickening whether these two terms were logically implied by each other that was they were referring to valid whether this statement that i am saying is valid that is they it it is logically uh what you can say implied okay if i have to remove it first let me .

Do this simplification then i explain you the difference between the two questions okay just let me do this one so this will be then we have here negation p that is negation p or negation q or r you are okay so this will become p this .

Will change into dot this will change into q complement and this will change into r complement plus this will change into p complement plus q complement plus r now now you can see here that if i take this q complement common from these two terms to k if i take q complement common so i'll get q .

Complement only so the resultant will be q complement plus p complement plus r if this is my result if this is my result so now it can either be true or false i will not get all times true values why because if my value of q .

Is true tk if p is also true and if r is false if this is the case in the truth table so what will be the result of this value the resultant of this will become what this will become false plus false plus false the result will come out to be false right so this question is basically .

Satisfiable it is not valid it is satisfiable okay now you have tried you have tried to solve it with that method that is your resolution okay let's try we have we have to basically imply a cheese okay so we have negation p when you have two terms and these are .

That are connected with the help of and you're getting my point everyone here this is one term and there is no and there is no connection there is no two different arguments or propositions that are connecting this okay so here you will not apply that resolution method y because this is one simple premise one .

Single premise okay and when you apply a resolution there has to be two premises at least now here you are only having one premise and that is also simple so obviously yet versatile if you see there are different different terms but when you have no other premise how you .

Will find the resolution you're getting my point everyone i hope i'm clear with my point what i'm trying to explain yes you cannot apply resolution why because in when we were talking about resolution in the previous cases in the previous questions that we were talking .

What was the case we were having premises we were having at least two three premises and what we were doing we were applying premise one then this premise two then premise three and then we were checking whether they are equal to this thing or not right this we were doing here what .

Happened is this is the single premise that we are having so with which we will check how we will find the connection between two different promises see whether this is logically implied or not second you have to open this implication no so when you will open this implication this .

Whole term will tone will have a compliment on its own nappy complement liquor i hope this is clear kt i'll write it more correctly in case tk so this is the difference between so that's nice i have taken this question otherwise you must have got confused other examples .

Okay so this is why you will not apply resolution here for resolution you should have at least two three clauses or premises okay so when you have this simple type of question directly go with the what you can say simplification method only nothing else will work in this method okay .

Yes so i was asking about that analysis one do you want to have an analysis video do you want a basic general video we will not discuss the questions we'll discuss the topics and we will discuss uh the strategy we can say or we can say key how we can uh study different different .

Topics so do you want a video like that so that's then i'll plan if it is okay then nobody's till then let me see how p q r okay what happened here is if you see this thing um yeah right okay wait i'll write over here you have to try to .

Understand this thing what is it in here this is written as p q complement r complement plus p complement plus q complement plus r okay so if you remember whenever we have questions to solve what we do is basically we have if this thing that is a plus .

A b c ticket so what we do here is we take a common right we take a common and then we have 1 plus b c so when i have told you already when you will add anything to one one basically represents true value so when you add anything to true value you will get true only and when you multiply anything with one .

You will get that digit that number itself okay so what will happen here is in among from these two terms that is q complement and p q complement r complement what you can do take q complement common so what you will get you will get p r complement plus one plus .

Le rest all co s then this will come what this will become same like this so you will get q complement plus p complement plus r clear swap nali i hope now it is clear to you okay tk so i'll uh plan a session of that type okay and then i'll tell you when we will .

Have that type of session i think maybe monday maybe maybe right maybe on monday we'll keep a session like this my mother because it will help everyone so okay my first step is this will go here also this will become .

Negation p this will go on this also so it will become or and this will go on this also it will become negation queue foreign because of certain reasons i'm not able to take the class but generally i did too .

I tried to take the class regularly only beat me one two days maybe one day maybe skipped but i take the class regularly only so tomorrow that is all for today ticket today uh actually this is all in proposition logic there's nothing else in proposition logic now uh what we will do tomorrow we will .

Have a class on predicate logic okay so now we will from tomorrow we'll start the predicate one and we'll see telegram group me okay uh this is the telegram uh what you can say i'll show you the telegram link so tomorrow we'll start with the .

Predicate logic and we'll practice the questions predicate logic is sometimes bit complicated but it is also easy sometimes it is logically thought out for the text so much now okay so friday we have a predicate logic and if possible we will try to have a class of on saturday also .

Of predicate logic only okay and then we'll see how we will proceed forward from the next week i'll discuss with you all and then we'll see okay yeah uh so this is the telegram channel that you can join that is uh t dot me slash netria yes kt i'll send today i'll give the pdf .

Today okay so this is the telegram link and then so tomorrow now we'll meet tomorrow at 6 00 p.m shop tickets experiment classic predicate logic is to do prepare the concepts of predicate logic because uh i won't be teaching from the basics tickets for basics whatever conscious we'll have in the .

Question we'll discuss those okay so that's all for today so welcome thank you thank you so much everyone take care okay bye bye good night