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If P and Q are two statements, then which of the following compound statement is a tautology ?

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in Mathematics by (35.0k points)

If P and Q are two statements, then which of the following compound statement is a tautology ?

(1) ((P ⇒ Q) ∧ ~ Q) ⇒ Q

(2) ((P ⇒ Q) ∧ ~ Q) ⇒ ~ P

(3) ((P ⇒ Q) ∧ ~ Q) ⇒ P

(4) ((P ⇒ Q) ∧ ~ Q) ⇒ (P ∧ Q)

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1 Answer

+1 vote
by (34.5k points)

Correct option is (2) ((P ⇒ Q) ∧ ~ Q) ⇒ ~ P

LHS of all the options are some i.e.

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