If Ram studies, he will pass his exam. Ram fails the exam. Which of the…

Solution: Use the contrapositive of the conditional statement.

Let S be "Ram studies for the exam" and P be "Ram passes the exam".

We are given S → P (if Ram studies then he will pass) and that Ram failed, i.e. not P.

The contrapositive of S → P is not P → not S, which is logically equivalent to the original conditional. From not P we can therefore conclude not S.

Hence, Ram did not study for the exam.

• The statement "Ram studied for the exam" is false because it contradicts the conclusion that he did not study.

• The statement "Ram may or may not have studied for the exam" is incorrect because we can determine he did not study.

• The statement "None of these" is incorrect because the statement "Ram did not study for the exam" follows from the premises.