Question

Which of the following statements is logically equivalent to: "If he studies, he will pass the course."

(A) He passed the course; therefore, he studied.
(B) He did not study; therefore, he will not pass the course.
(C) He did not pass the course; therefore he did not study.
(D) He will pass the course only if he studies.
(E) None of the above.

Answer 1

There are three types of statements:

1. Contrapositive

2. Inverse

3. Converse

Let's test each of them out.

1. Contrapositive would be he did not pass the course, and he did not study.

2. Inverse would be if he did not study, he did not pass.

3. Converse would be if he did not study, he will not pass.

Our answer is option C because it is an inverse statement. If he does not study, he does not pass the course.