jee-main 2021 Q68

jee-main · India · session2_18mar_shift2 Proof True/False Justification

If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?
(1) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow Q$
(2) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow \sim P$
(3) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow P$
(4) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow ( P \wedge Q )$

If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?\\
(1) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow Q$\\
(2) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow \sim P$\\
(3) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow P$\\
(4) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow ( P \wedge Q )$

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