Question

Let q(n) be the predicate "n2 ≤ 30."
a. write q(2), q(−2), q(7), and q(−7), and indicate which of these statements are true and which are false.
b. find the truth set of q(n) if the domain of n is z, the set of all integers.
c. if the domain is the set z+ of all positive integers, what is the truth set of q(n)?

Answer 1

For n=2 we get "4≤ 30"
For n=-2 we get "4≤ 30"
For n=7 we get "49≤ 30"
For n=-7 we get "49≤ 30"
b) We have to solve the equation like this:
$n^2\leq30\iff n\leq\sqrt{15}\iff n\leq 3.8$
So the set truth is all integers less than or equal to 3. 
c)When the domain is the set Z+, then we get the set:
$q(n)=\{0,1,2,3\}$