Predicates and Quantifiers in discrete math. Let P(x,y) be "x is waiting for y", where the universe of discourse is the set of all people in the world. Use quantifiers to express the following statement. (i)There is no one who is waiting for everybody. (ii) Everybody is waiting for somebody. May i know how to solve this kind of question?

sincsenekdq

sincsenekdq

Answered question

2022-09-07

Predicates and Quantifiers in discrete math
Let P(x,y) be "x is waiting for y", where the universe of discourse is the set of all people in the world. Use quantifiers to express the following statement. (i)There is no one who is waiting for everybody. (ii) Everybody is waiting for somebody.
May i know how to solve this kind of question?

Answer & Explanation

Peyton Atkins

Peyton Atkins

Beginner2022-09-08Added 13 answers

Step 1
(i) "There is no one who is waiting for everybody." Meaning: There does not exist a person (i.e., x) who is waiting for everybody (i.e., y). Thus, for (i), we get the following: x y P ( x , y ). However, you may want to report the answer without any negated quantifiers; in such a case, you may observe the following:
¬ ( x y P ( x , y ) ) = ( ¬ x ) ( y ) ¬ P ( x , y ) = x y ¬ P ( x , y ) ,
where ¬ P ( x , y ) is taken to mean "x is not waiting for y."
Step 2
(ii) "Everybody is waiting for somebody." Meaning: There exists someone (i.e., y) who is being waited for by everyone (i.e., x). Thus, the reported answer for (ii) would be y x P ( x , y ). Note that the order of quantifiers is important here.

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