Contrapositive Examples

Stimulus:

"If a person is a doctor, then they have a medical degree."

Question Stem:

Which of the following is logically equivalent to the statement above?

A) If a person is not a doctor, then they do not have a medical degree.
B) If a person has a medical degree, then they are a doctor.
C) If a person does not have a medical degree, then they are not a doctor.
D) If a person is a doctor, then they do not have a medical degree.
E) If a person is a doctor, then they have a PhD.

Correct Answer:

C) If a person does not have a medical degree, then they are not a doctor.
This is the contrapositive of the original conditional. It flips both the terms (doctor → medical degree) and negates both.

Contrapositive:

"If a person does not have a medical degree, then they are not a doctor."

Stimulus:

"If it is raining, then the ground will be wet."

Question Stem:

Which of the following must be true if the statement above is true?

A) If it is not raining, then the ground is dry.
B) If the ground is not wet, then it is not raining.
C) If the ground is wet, then it is raining.
D) If it is raining, then the ground is wet.
E) If the ground is not wet, then it is not raining.

Correct Answer:

B) If the ground is not wet, then it is not raining.
This is the contrapositive of the original statement. It negates both the condition ("raining") and the result ("wet").

Contrapositive:

"If the ground is not wet, then it is not raining."

Stimulus:

"If someone studies for the test, then they will pass."

Question Stem:

Which of the following statements is logically equivalent to the statement above?

A) If someone studies for the test, then they will pass.
B) If someone did not study for the test, then they will fail.
C) If someone does not pass, then they did not study for the test.
D) If someone passes, then they studied for the test.
E) If someone does not study for the test, then they will fail.

Correct Answer:

C) If someone does not pass, then they did not study for the test.
This is the contrapositive of the original conditional. It negates both "studies" and "passes."

Contrapositive:

"If someone does not pass, then they did not study for the test."

Stimulus:

"If the meeting is scheduled, then the conference room will be reserved."

Question Stem:

Which of the following is equivalent to the statement above?

A) If the meeting is scheduled, then the conference room will not be reserved.
B) If the conference room is reserved, then the meeting is scheduled.
C) If the meeting is not scheduled, then the conference room is not reserved.
D) If the conference room is not reserved, then the meeting is not scheduled.
E) If the meeting is scheduled, then the conference room is reserved.

Correct Answer:

D) If the conference room is not reserved, then the meeting is not scheduled.
This is the contrapositive of the original statement.

Contrapositive:

"If the conference room is not reserved, then the meeting is not scheduled."