Let a(x, y), b(x, y,) and c(x, y) be three statements with variables x and y…
GATE · 2004 · IT
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)]
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