Chapter 1, Problem 21SE

LetP(m,n) be the statement “mdividesn," where the domain for both variables consists of all positive integers. (By "mdividesn" we mean that $n=\text{km}$ for some integerk.) Determine the truth values of each of these statements.

a) $P\left(4,5\right)$

b) $P\left(2,4\right)$

c)

   $\forall m\forall nP\left(m,n\right)$

d) $\exists m\forall nP\left(m,n\right)$

e) $\exists n\forall mP\left(m,n\right)$

f) $\forall nP\left(1,n\right)$