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UGC-NET | UGC NET CS 2015 Dec – II | Question 7
  • Last Updated : 01 May, 2018

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 the following propositions.
(a)∃m ∀n P(m, n)
(b)∀n P(1, n)
(c) ∀m ∀n P(m, n)
Codes :

(A) (a) – True; (b) – True; (c) – False
(B) (a) – True; (b) – False; (c) – False
(C) (a) – False; (b) – False; (c) – False
(D) (a) – True; (b) – True; (c) – True


Answer: (A)

Explanation:

  • ∃m ∀n P(m, n) : There exist some m which divides all n.True
  • ∀n P(1, n) Every n divided by 1.True
  • ∀m ∀n P(m, n) Every m divides every n False

So, option (A) is correct.

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