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December2015 Cs Q7

0. Let P(m, n) be the statement "m divides n” where the Universe of discourse for both the variable 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)

  • Option : 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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