UGC-NET | UGC NET CS 2015 Dec – II | Question 7

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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