Question

# The contrapositive of the following statements, ”If the side of a square doubles, then its area increases four times” is:A) If the area of a square increases four times, then its side is not doubledB) If the area of a square increases four times, then its side is doubledC) If the area of a square does not increase four times, then its side is not doubledD) If the side of a square is not doubled, then its area does not increase four times

Hint:Contrapositive of the statement in the form $p \to q$ is given by $\sim q \to \sim p$. Here $p$ represents sides of square get doubled and $q$ represents its area increases four times.

So in the logic, contrapositive of a conditional statement is formed by negating both terms and reverting the direction of inference. Let us explain by example. Suppose the statement is given as “If A then B” which means $A \to B$ these are conditional statements, so this statement explains the contrapositive given by $\sim B \to \sim A$. In the statement “If not B, then not A”. Thus this is contrapositive of the statement.
So we can write the statement as $p \to q$ and its contrapositive statement is given by $\sim q \to \sim p$.