Question

The contrapositive of the statement ‘I go to school if it does not rain’ is :
A. If it rains, I do not go to school.
B. If I do not go to school, it rains.
C. If it rains, I go to school.
D. If I go to school, it rains.

Answer 1

Hint:- We had to only use the identity of mathematical reasoning which states that if p implies q i.e. $p \Rightarrow q$, then its contrapositive will be negation of q implies negation of p i.e. $\sim q \Rightarrow \sim p$, where p and q can be statements, true and false.

Complete step-by-step solution -
As we know that the contrapositive of A implies B will be equal to not B implies not A.
And in other words, the contrapositive of if A, then B will be equal to not B, then not A.
So, we had to split the given statement into two different statements A and B.
So, let A be “I go to school.”
And, B will be “If it does not rain.”
Now let us find the negation of statements A and B.
As we know that the negation of any statement is the statement which is opposite the meaning of the original statement or we can say that we had to make the given statement false. So, that can be done by using not in the statement if it is not present and removing not if it is present in the given statement.
So, $\sim A$ (negation of A) will be “I do not go to school.”
And, $\sim B$ (negation of B) will be “if it rains.”
So, now as we have stated above, the contrapositive of $A \Rightarrow B$ is $\sim B \Rightarrow \sim A$.
And we know that $\Rightarrow$ stands for implies which can be written by using comma or then between two statements.
So, $\sim B \Rightarrow \sim A$ will be “If it rains, I do not go to school.”
Hence, the contrapositive of the statement “I go to school if it does not rain” will be “If it rains, I do not go to school”.

Note:- Whenever we come up with this type of problem where we are asked to find the contrapositive of the given statement then first, we had to split the given statement into two different meaningful statements (like A and B) and then we had to find the negation of the both statements by adding or removing not in the statement. After that the contrapositive of the given statement will be equal to the negation of the second statement (B) implies the negation of the first statement (A). And to apply implies we can just place a comma between the negation of both statements (B and A).