00:02
The question is to use quantifiers represented as q to express 8 statements.
00:09
Here, t of x y represents the statement x allows y, where x and y belongs to the set d, where t is the set of all people in the world.
00:23
The quantifiers q are of two types, universal quantifiers represented as u and existential quantifiers represent as e.
00:34
The universal quantifier is for all denoted as and the existential quantifier is there exist denoted as.
00:52
So the universal quantifier represents that every element of a set follows a particular property while the existential quantifier indicates that at least one element of the set of the set satisfies the particular property.
01:12
Here the first statement is everyone loves everyone.
01:17
So this is the use of the universal product.
01:21
So everyone loves everyone means for all xy element of d p of x that means every person in the world satisfies this property.
01:33
So everyone loves everyone.
01:37
The next statement is for every everyone loves them.
01:42
This is also the usage of universal quantifier.
01:46
So for everyone in the world, that person loves himself.
01:51
So for all x element of p p of x x.
01:55
So for everyone, everyone loves them.
01:59
The next statement is everyone loves someone.
02:04
Now this is a combination of both the quantifiers.
02:07
So everyone loves someone means for all x element of that is everyone there exists a person or at least one person such that be of x one so that means everyone loves someone the next statement is there is someone who is loved by everyone so this is also a combination statement so there exist a person who is loud by everyone so there exists a y element of d such that for all x element of d p of x -y...