Answer to Question #242108 in Discrete Mathematics for Erick

Question

(i). In MA161 class, the lecturer gave the following proposition. Let A (x, y) be “ y is greater than or equal to x ”. The domain for the proposition is the set of nonnegative integers. The students were tasked to determine what are the truth values of ∃y ∀xA (x,y) and ∀x∃yA(x,y ) ?

Answer 1

Part 1

The statement says that for every non-zero real number, there exists a real number such that their product equals 1, this is the inverse property of multiplication and thus always true. Hence the statement is true.

Hence, the Truth value of this statement is True.

Part 2

The statement says that there exists a real number such that every non-zero real number does not exist and thus the statement is false.

Hence, the Truth value of this statement is False.