## Discrete Mathematics with Applications 4th Edition

The statement is false when $a=-1$.
Written in standard english, the logical statement $\forall a\in \mathbb{Z},\frac{a-1}{a}\text{ is not an integer}$ means "for all numbers $a$ in the set of integers, $\frac{a-1}{a}$ is not an integer." When we plug $-1$ in for $a$, we get $\frac{-1-1}{-1}=\frac{-2}{-2}=2$, which is an integer. Therefore, the statement is false when $a$ = $-1$.