hi all of you welcome back to ramadin maths academy okay sorry for all uh because uh e4 friday's new videos posted because of the wi-fi and uh some another problems okay and don't need to worry about madame videos a proposed just arrow exams okay don't worry i'm here to help you but logic and proofs means discrete mathematics first chapter logical equivalence truth tables five videos chess you know this is the sixth lecture in our discrete mathematics logic and proofs today's topic is predicates first of all what is the predicate actually in logical groups we have two types of logics is there one is the logically a propositional logic and another one is the predicate logic okay here today we are going to discuss the predicate it's very simple no need to worry you probably couldn't find videos of a question and predicates too and uh remaining videos but be careful this is a very most important topic in your first chapter in discrete mathematics okay now uh you put a predicate i said what is the predicate predicate and then we suppose i'll consider one statement listen carefully it's very important suppose x is greater than 3 beta x is greater than 3 then what is the predicate and how we are defined this suppose in terms of how we can write x greater than 3 x is greater than 3 x is a variable one is the variable another one is the logic that is see this x is the variable now that is called the subject that is called the subject of the statement and greater than three e greater than three months that is the predicate of the statement the nuance logic is it clear x is greater than three here x is the subject and three is greater than three this is our predicate okay statement even right now p of x is nothing but the predicate p is what better predicate okay x is what that is a variable okay x is what the variable we can define the statement like this also now i'll give uh some examples of predicates [Music] sometimes either it may be true or it may be false depends upon the statement okay let p of x denotes the statement x is greater than three and a germany gamma naturally x is greater than three okay what are the truth values of p r four and p of two and to narrow actually first of all what is the predicate of the statement we already discussed what is the predicate here then predicate any more to the beta x greater than three k p of x is the predicate here p is the predicate and x is a variable okay our predicate is greater than three if you consider in the place of p and event nano this is what this is what is a given statement here how we can write the predicate is what x greater than three the predicate is what the predicate is x greater than three and they can even each have to find out p half 4 we can write x greater than 3 in terms of the predicate we can write p of x okay if you consider p of 4 means in the place of x what we have to do substitute 4 then it will become 2 if you consider p of 4 if p of 4 and 20 then x is equal to 4 x is equal to 4 this 4 is greater than 3 means what p of 4 is a true this this is having truth value okay or else you can write it is false therefore therefore p of 4 is true what is the truth value of this p of 4 is true then check it p of 2 okay we have 2 we have to ante explicitly in this call new to this quality what is our statement x is greater than three if you consider two is greater than three a one two nano x is e or else you can write x is equal to 2 in the predicate logic then 2 is greater than 3 this is what which is wrong statement 2 is greater than 3 no therefore when we even write minimum therefore p of 2 is false is not false like that you can verify whether the statement is true or false by using predicate logic and one more example an important one is qr fix denotes the statement x is equal to y plus 3 this is x is equal to y plus 3 listen carefully what are the truth values of proposition q of 1 comma two q of three comma zero first of all the given logic you can write in terms of predicate eighth german key x is equal to y plus three we need to predict what is the given statement here ah they already defined in terms of q along the x and y log the and then the the function the predicate logic it defines in terms of it could be of x law denote this requirement narrow q of x comma y here x and y are the variables what is the condition the condition is x is equal to y plus 3 that is the predicate in that case what we have to do now i will going to consider this here my logic intended what is the given one here x is equal to y plus 3 here what is our x value x is equal to 1 and y is equal to 2 put here what will happen this is 2 plus 3 this is what 1 is equal to 5 no it is a false then you can write it as it is a false therefore therefore q of 1 comma 2 the predicate is false like that you can write the truth values of the predicates now consider this here x is equal to what 3 y is equal to what 0 then how we are going to write what is the statement y is equal to x is equal to y plus 3 3 is equal to what beta here y is 0 3 both are same and the empty the statement predicate logic sometimes either it may be true or it may be false okay therefore in dq zero is true in the predicate logic is it clear just note okay it statement in predicate logic in that compound statement means we have two or more statements or minimum two statements is there by using our connectives what is our connectives conjunction disjunction and implication by implication by using these four you have to write the combination of those statements that is the compound statement of the predicates statements a teacher her teaching is good this is one statement and this is another statement here what we have to do in ehm understand the first statement rama is a teacher and her teaching is good i'm contented antibodies over here what is our connective conjunction what is that anthony indicate then condom on the first of all you have to identify which is the subject and which is the predicate in the given statement [Music] that is what our subject rama is a subject then what is ramay's teacher teacher means it indicates the logic that is what it it is what predicate predicate and in even write you or we can write it as predicate logic and then the predicate teacher predicate me teacher okay and her teaching is good and here teaching is the subject teaching is the subject good is the predicate okay then how we are going to write predicate logic is what it stands good then what is the variable here teaching means you can write t like this okay this is what the compound statement how we are going to write the compound statement by using the connective also kind or then or if and only we already know that how we are going to write the predicate rama is a teacher rama is the variable subject and t is the teacher predicate or r means like this her teaching is good means or teaching is the subject good is the predicate means what g of t then even i cho t of r then then and entry like this implies g of t okay like that we can write the compound statements of the predicates next we will discuss the quantifiers okay see all of you next and most important one is the quantifier quantifier statement quantifier and the intent suppose just just observe these four statements okay or prepositions anything all students have books okay all students having books that is one statement and some moments are tall or short now whatever it may be but here hall and some it could have no one sit in the class no one for every integer x x square is non-negative integer in these four statements in this four statement all some know one for every each and every statement indicates by using these four values these four terms those terms are called it as quantifiers you know in this statement all sum no one there exist or for every like that that is associated with some quantity or with some statement those statements are called it as what quantifiers in the quantifiers we have two types one is the universal quantifier then another one is the existential quantifier now we will discuss what is universal quantifier and what is the existential quantifier law see all of you here universal quantifier universal quantifier but for all all values and this kundalini call it that is universal i want to know the universal quantifier of p of x is the statement what is the statement here p of x for all values of x and the universal law for all values and you mentioned just arrow in the domain d for example [Music] is the universal quantifier of the predicate p of x and here for all is called what universal quantifier this is the universal quantifier here we read it as for all p x or else for every x p x and j for example i'll consider one small statement p of x this statement x plus 1 greater than x what is the truth values of the quantifier for all x p of x where the domain consists for all the real numbers and into the the given statement of the predicator p of x is what x plus 1 is greater than x okay that is the given statement then how we are going to write the quantifier p of x is true why because for all values of the real numbers you know the statement which when it is true uh of the quantifier all the real values and payment render this is the statement if you consider the quantifier of the statement in terms of pr x it is true for all true for all the real numbers x is for all real numbers the quantifier for all x p x is true okay like that you can write the universal quantifiers now next we'll discuss the existential quantifiers okay now down see existential quantifier and indent then there exist at least one element in the given statement for example i will consider qr fix denotes the statement what is our statement x is equal to x plus 3 and here what is the truth values of the quantification of there exist x belongs to q of x where the domain consists for all real numbers what is our given statement first you have to write the given statement consider it as p q of x for your wish p of x okay that is one statement x is equal to x plus 3 then q of x is true when it is for all real numbers okay if you take for all real numbers the statement is true if you take one then it will what will happen one is equal to what one is equal to had one plus three and demo one is equal to four both are equal no for all real numbers it is not true and the rexist x q of x is false means this is not existence okay this is the existential quantifier [Music] thanks for watching