Q34,paper 2,D13. Let P(m, n) be the statement “m divides n” where the universe of discourse for both the variables is the set of positive integers. Determine the truth values of each of the following propositions :

I. ∀m ∀n P(m, n),

II. ∃m ∀n P(m, n)

(A) Both I and II are true .

(B) Both I and II are false .

(C) I – false & II – true

(D) I – true & II – false

Answer C.

Explanation.

Statement 1 say . all integer divides all integer. Which is false.

Statement 2 say . there exists an integer which divides all integer.

Integer 1 divides all numbers. Statement 2 is true.

Hence option C.