Mathematical Reasoning: The statement sim(p rightarrowsim q) is equivalent to | JEE Main 2021

JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 1

The statement $\sim(p\leftrightarrow\sim q)$ is equivalent to

Mathematical Reasoning

$p\leftrightarrow q$✓ Correct answer$p\leftrightarrow\sim q$$\sim q\to p$$\sim p\wedge q$

Solution

$p\leftrightarrow\sim q$ is true exactly when $p,q$ differ, so its negation is true when they agree: $\sim(p\leftrightarrow\sim q)\equiv p\leftrightarrow q$.

Mathematical Reasoning - JEE Mathematics question (JEE Main 2021 (Online) 3rd August Evening Shift)

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