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WAEC Mathematics 2022 Question 15

Question 15

Logic

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

  1. A.If Stephen is good at Mathematics, then he is intelligent.
  2. B.If Stephen is not good at Mathematics, then he is not intelligent.
  3. C.If Stephen is not intelligent, then he is not good at Mathematics.
  4. D.If Stephen is not good at Mathematics, then he is intelligent.
Show the answer and explanation

Answer: B (If Stephen is not good at Mathematics, then he is not intelligent.)

Explanation

p ⇒ q always has the same truth as its contrapositive ~q ⇒ ~p: if he is not good at Mathematics, he is not intelligent.