Statement 1: (p ≤ftrightarrow q) is equivalent to p ≤ftrightarrow q . Statement 2: (p ≤ftrightarrow q) is a tautology. - Mathematics MCQ AIEEE 2009 2026 | ExamTest.live

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1 mark

Statement 1: \sim (p \leftrightarrow\sim q) is equivalent to p \leftrightarrow q . Statement 2: \sim (p \leftrightarrow\sim q) is a tautology.

A $Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1$
B $Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1$
C $Statement-1 is true, Statement-2 is false$
D $Statement-1 is false, Statement-2 is true$

Solution & Step-by-step Explanation

p \leftrightarrow q is true when p, q are same. p \leftrightarrow\sim q is true when p, q are different. \sim (p \leftrightarrow\sim q) is true when it's not the case that p, q are different ⟹ p, q are same.This is equivalent to p \leftrightarrow q . Statement-1 is true.Statement-2 says it's a tautology. p \leftrightarrow q is not a tautology (it can be false).Thus Statement-2 is false.

Try it yourself before checking the explanation above.

Statement 1: \sim (p \leftrightarrow\sim q) is equivalent to p \leftrightarrow q . Statement 2: \sim (p \leftrightarrow\sim q) is a tautology.

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

Statement-1 is true, Statement-2 is false

Statement-1 is false, Statement-2 is true

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