Mathematical Reasoning * — JEE Main · 2009 · 12 Apr 2009 · Offline Question with Solution

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✓ Correct
(D)Statement-1 is false, Statement-2 is true

Answer: (C)

Solution

Building a truth table for

p

and

q

, the column for

\sim (p \leftrightarrow\sim q)

comes out true, false, false, true, which is exactly the column for

p \leftrightarrow q

, so the two are equivalent and the first statement is true. That same column is false in two of the four rows, so

\sim (p \leftrightarrow\sim q)

is not always true and hence not a tautology, making the second statement false.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option