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Question

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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
Verified

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.