Proposition: $\exists n \in \mathbb{Z} $ such that $\forall m \in \mathbb{Z}, m<n $.
a) Negate the statement of proposition.
b) Disprove proposition
Here is what I wrote:
a) $\forall n \in \mathbb{Z}, \exists m \in \mathbb{Z}, m >= n$.
b) The statement says "there exists an integer n, such that for every integer m, m is less than n." As a counterexample, let n = 1. For every element in the integers, m, must bust be less than n. This may be true for some cases, but not all cases of m. Let us show that, when m=2, 2 < 1 is not a true statement. Hence, disproven.
What did I do wrong here? I only received partial credit. How do I disproove this? Did I get part A correct at least?