GATE | GATE-IT-2004 | Question 3
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:
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