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 doubled
B) If the area of a square increases four times, then its side is doubled
C) If the area of a square does not increase four times, then its side is not doubled
D) If the side of a square is not doubled, then its area does not increase four times

Answer 1

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.

Complete step-by-step answer:
Here a statement is given that if sides of a square get doubled then its area becomes four times. And we are asked to find its contrapositive statement.

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 similarly here is a conditional statement saying If the side of a square doubles, then its area increases four times.
So let p represent sides of a square gets doubled and q represent area becomes four times.
So we can write the statement as $p \to q$ and its contrapositive statement is given by $\sim q \to \sim p$.
That means if the area of a square does not increase four times then its side is not doubled.

So, the correct answer is “Option C”.

Note: You might be wondering that the contrapositive is the negation of the given statement but no you are wrong. A statement and its contrapositive are logically equivalent, in the sense that if the statement is true, then its contrapositive is true and vice versa.