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GATE | GATE-IT-2004 | Question 3
  • Last Updated : 29 Nov, 2015
Let a(x, y), b(x, y,) and c(x, y) be three statements with variables x and y chosen from some universe. Consider the following statement:

(∃x)(∀y)[(a(x, y) ∧ b(x, y)) ∧ ¬c(x, y)]

Which one of the following is its equivalent?

 
(A) (∀x)(∃y)[(a(x, y) ∨ b(x, y)) → c(x, y)]
(B) (∃x)(∀y)[(a(x, y) ∨ b(x, y)) ∧¬ c(x, y)]
(C) ¬ (∀x)(∃y)[(a(x, y) ∧ b(x, y)) → c(x, y)]
(D) ¬ (∀x)(∃y)[(a(x, y) ∨ b(x, y)) → c(x, y)]


Answer: (C)

Explanation:

Quiz of this Question

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