Mathematical Reasoning: If P and Q are two statements, then which of the following compound… | JEE Main 2021

JEE Main 2021 (Online) 18th March Evening ShiftQuestion 1

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

Mathematical Reasoning

$((P\Rightarrow Q)\wedge\sim Q)\Rightarrow P$$((P\Rightarrow Q)\wedge\sim Q)\Rightarrow Q$$((P\Rightarrow Q)\wedge\sim Q)\Rightarrow\sim P$✓ Correct answer$((P\Rightarrow Q)\wedge\sim Q)\Rightarrow(P\wedge Q)$

Solution

$((P\Rightarrow Q)\wedge\sim Q)\Rightarrow\sim P$ is modus tollens, a tautology. Antecedent is true only for $P=Q=F$, where $\sim P$ is true but $P$, $Q$, $P\wedge Q$ are false.

Mathematical Reasoning - JEE Mathematics question (JEE Main 2021 (Online) 18th March Evening Shift)

More from Mathematical Reasoning