Consider the statements: p: Stephen is intelligent q: Stephen is good at Mathematics If p⇒q, which of the following is a valid conclusion?

Analyze the question

We are given the conditional statement p ⇒ q, meaning "If Stephen is intelligent, then he is good at Mathematics." We need to find which statement must logically follow from it.

Concept: Related conditional statements

For p ⇒ q:

• Converse: q ⇒ p (not necessarily valid)
• Inverse: ~p ⇒ ~q (not necessarily valid)
• Contrapositive: ~q ⇒ ~p (always logically equivalent to the original, so it is valid)

Check each option

• A. "If Stephen is good at Mathematics, then he is intelligent" is q ⇒ p. This is the converse, so it is not valid.
• B. "If Stephen is not good at Mathematics, then he is not intelligent" is ~q ⇒ ~p. This is the contrapositive, so it is valid.
• C. "If Stephen is not intelligent, then he is not good at Mathematics" is ~p ⇒ ~q. This is the inverse, so it is not valid.
• D. "If Stephen is not good at Mathematics, then he is intelligent" is ~q ⇒ p. This does not follow from p ⇒ q.

Answer

The contrapositive, option B, is the only valid conclusion.

Tip: To find the contrapositive, swap the two statements and negate both: p ⇒ q becomes ~q ⇒ ~p. Remember, "flip and negate." The converse and inverse are traps that WASSCE, NECO, and JAMB love to include as wrong options.