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
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.
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.