Finding the contrapositive of the statement "I go to school if it does not rain"

Question

I got this question in a exam.There were two more statements in the examination(but they were quite clearly wrong).However I got stuck between these two statements.The contrapositive of the the statement "I go to school if it does not rain" is

$(1)\qquad$If it rains, I do not go to school

$(2)\qquad$If I do not go to school it rains

Which of the two options would be correct by mathematical reasoning.

Answer 1

The contrapositive of $A$ implies $B$ is not $B$ implies not $A$.

In other words, the contrapositive of if $A$, then $B$ is if not $B$, then not $A$.

Answer 2

You can rephrase the statement in the standard 'if p then q' form: "If it does not rain, then I go to school." The contrapositive is 'if not q then not p'. That is in this case "If I do not go to school, then it rained."

Note that the contrapositive of a statement is logically equivalent to that statement.