Let P(m,n) be the statement "m divides n" where the universe of discourse for both variables is the set of positive integers. Which of the following propositions is FALSE?

(a) P(2, 4)
(b) ∃m∀nP(m,n)
(c) ∀m∀n P(m,n)
(d) ∀n P(1,n)
(e) None of the above

Question

Let P(m,n) be the statement "m divides n" where the universe of discourse for both variables is the set of positive integers. Which of the following propositions is FALSE?

(a) P(2, 4)
(b) ∃m∀nP(m,n)
(c) ∀m∀n P(m,n)
(d) ∀n P(1,n)
(e) None of the above

anonymous · Answer

(C). since for all m and for all n, it is not possible that m divides n.

anonymous · Answer

wouldn't you say D? since i don't think it's possible for 1 to be divisible by any number...right?

anonymous · Answer

No, m divides n
       1 divides n
1 always divides any number.

anonymous · Answer

even infinity? it still counts as positive integer right?