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

Answer: (B)

If I do not go to school, it rains.

In the given statement, let $p$ denote the part "it does not rain"

and $q$ denote the part "i go to school"

So the given statement is $p⟶q$

Now for a contrapositive statement, by definition we have

$(p⟶q)\leftrightarrow (\sim q⟶\sim p)$

So $\sim q$ means "i do not go to school"

and $\sim p$ means "it rains"

$\sim q⟶\sim p$ means "if i do not go to school, it rains"