 QUESTION

# Contrapositive of the statement “If two numbers are not equal, then their squares are not equal”, is:A. If the squares of the two numbers are equal, then the numbers are equal.B. If the squares of two numbers are equal, then the numbers are not equal.C. If the squares of two numbers are not equal, then the numbers are not equal.D. None of these

Hint: In logic and mathematics, the contrapositive of a conditional statement of the form “If $p$ then $q$” is “If $\sim q$ then $\sim p$”. Symbolically, the contrapositive of $p \to q$ is $\sim q \to \sim p$. So, take the first statement as $p$ and the second statement as $q$ and find the contrapositive as stated above. So, use this concept to reach the solution of the given problem.

Let the first statement i.e., If two numbers are not equal is $p$
And the second statement i.e., their squares are not equal is $q$
Now the total statement is given by $p \to q$
We know that the contrapositive statement of $p \to q$ is $\sim q \to \sim p$.
The negative statement of $q$ i.e., $\sim q$ is If the squares of two numbers are equal
The negative statement of $p$ i.e., $\sim p$ is the two numbers are equal
Hence the contrapositive statement $\sim q \to \sim p$ is given by “If the squares of the two numbers are equal, then the numbers are equal”.