Truth Value Of Statements

Bashyboy
The question is, "Determine the truth value of each of these statements if the domain consists of all integers?"

The statements are:

$\forall n(n^2 \geq 0)$

$\exists n(n^2=2)$

$\forall n(n^2\geq n)$

$\exists n(n^2 less than 0)$

Does it seem, from reading the question, that I am to determine the truth value of the statement by simply looking at it, or is there some proving process involved?

For example, to prove that $n^2 \geq 0$ is true for all integers $n$, try considering the following three cases separately: $n > 0$, $n = 0$, $n < 0$.