Question

Contrapositive of the statement "If a quadrilateral is a square, then it has two pairs of parallel sides".

• A. If a quadrilateral has two pairs of parallel sides, then it is a square.
• B. If a quadrilateral is not a square, then it does not have two pairs of parallel sides
• C. If a quadrilateral does not have two pairs of parallel sides, then it is not a square.
• D. If a quadrilateral is a square, then it does not have two pairs of parallel sides

Answer 1

The correct option is C If a quadrilateral does not have two pairs of parallel sides, then it is not a square.

For any conditional staements $p\to q$
Converse statement is $q\to p$
Inverse statement is $\sim p\to \sim q$
Contrapositive statement is $\sim q\to \sim p$
So, in this case
$p$= a quadrilateral is a square
$q$= it has two pairs of parallel sides
Contrapositive statement is $\sim q\to \sim p$
$\Rightarrow$ If a quadrilateral does not have two pairs of parallel sides, then it is not a square.