JEE Main 2013 Mathematics question

Not in JEE syllabus

Statement-1: The statement A → (B → A) is equivalent to A → (A ∨ B). Statement-2: The statement ∼ [(A ∧ B) → (∼ A ∨ B)] is a Tautology.

(1)Statement- 1 is false; Statement- 2 is true.
(2)Statement-1 is true; Statement-2 is true; Statement- 2 is not correct explanation for Statement-1.
(3)Statement-1 is true; Statement- 2 is false.Correct
(4)Statement-1 is true; Statement-2 is true; Statement- 2 is the correct explanation for Statement-1.

Answer: (3)

Solution

Both A → (B → A) and A → (A ∨ B) are tautologies, hence equivalent — Statement 1 true. (A ∧ B) → (∼A ∨ B) is always

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Question ID VK-103969