P(m, n) means "m ≤ n," where the universe of discourse for m and n is the set of nonnegative integers. What is the truth value of the statement?
-$$\exists n \forall m P ( m , n )$$

Question

Quizplus · Accepted Answer

The statement claims there exists a nonnegative integer $n$ such that for every nonnegative integer $m$, $m \leq n$. This is false because no matter what $n$ you choose, there will always be an $m$ (specifically, $m = n+1$) that is greater than $n$, violating the statement.

P(m, N) Means "M ≤ N," Where the Universe of Discourse