Question

STATEMENT 1: The contrapositive of the statement "If you have $6$ ice-creams, then you can eat in $6!$ ways" is "If you cannot eat in $6!$ ways, then you do not have $6$ ice-creams".
STATEMENT 2: Statement $p\Rightarrow q$ and its contrapositive are not logically equivalent.

• 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.

Answer 1

The correct option is C STATEMENT 1 is True, STATEMENT 2 is False.

The statement $\sim q\Rightarrow \sim p$ is called contrapositive of the statement $p\Rightarrow q$.
Statement : If you have $6$ ice-creams then you can eat in $6!$ ways.
Contrapositive : If you cannot eat in $6!$ ways then you do not have $6$ ice-creams
$\therefore$ Statement $p\Rightarrow q$and its contrapositive are logically equivalent.
Hence, STATEMENT-1 is True, STATEMENT-2 is False.