Question

Which of the following is the contrapositive of the following statement: If it is past 5:00 p.m., Megan’s office building is not empty

A: If Megan’s office building is empty, then it is past 5:00 pm.

B: If Megan’s office building is empty, then it is not past 5:00 p.m.

C: If Megan’s office building is empty, then it is past 5:00 p.m.

D: If it is not past 5:00 p.m. Megan’s office building is empty.

Answer 1

B

Explanation:

A contrapositive statement is one that switches the hypothesis and conclusion of a conditional statement and negates both. In our hypothesis,

"If it is past 5:00 p.m., Megan’s office building is not empty", we shall break it into two statements and show the contarpositive of each like shown below.

Hypothesis Contrapositive

Megan’s office building is not empty- Megan’s office building is empty

It is past 5:00 p.m - it is not past 5:00 p.m

And thus the contrapositive statement becomes

If Megan’s office building is empty, then it is not past 5:00 p.m.