# Truth Value Of Statements

• Bashyboy

#### 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?

If you can determine the truth by simply looking at it, that seems fine to me. If this is homework, you may want to write a brief explanation even if you could see that it was true by inspection. For example, for the first statement you might write "this square of any real number is ______, therefore this statement is _______"

What if I was to prove them? How would I go about that? Any hints? Would negating each statement be a good start?

Negation might be useful for some of these. Others will probably be more straightforward to prove directly.

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