WAEC 2016 Mathematics · Question 28

Which of following is a valid conclusion from the premise. "Nigeria footballers are good footballers"?

Options

  1. A.Joseph plays football in Nigeria therefore he is a good footballer
  2. B.Joseph is a good footballer therefore he is a Nigerian footballer
  3. C.Joseph is a Nigerian footballer therefore he is a good footballer
  4. D.Joseph plays good football therefore he is a Nigerian footballer

Answer: C. Joseph is a Nigerian footballer therefore he is a good footballer

Explanation written with AI and checked against the answer key

Analyze the question: This is a logic (validity of arguments) question. The premise is "All Nigerian footballers are good footballers." We need the conclusion that follows necessarily.

Concept: A statement "All A are B" means A is a subset of B.

  • If x is in A, then x is in B (valid).
  • If x is in B, we cannot conclude x is in A (invalid, since B may contain members outside A).

Here, A = Nigerian footballers, B = good footballers.

Check each option:

  • A. "Joseph plays football in Nigeria, so he is a good footballer." Playing football in Nigeria does not make someone a Nigerian footballer (he could be a foreigner), so this is not valid.
  • B. "Joseph is a good footballer, so he is a Nigerian footballer." This reverses the premise (B to A), so it is invalid. Good footballers exist in other countries too.
  • C. "Joseph is a Nigerian footballer, so he is a good footballer." Joseph is in A, and A is inside B, so Joseph is in B. This is valid.
  • D. "Joseph plays good football, so he is a Nigerian footballer." This is also the reversed (converse) form, so it is invalid.

Tip: In "All A are B" questions, only the argument that goes from A to B is valid. Beware of options that go from B back to A. This is the converse error, and examiners love to use it as a trap. Drawing a small circle (A) inside a bigger circle (B) quickly shows this.

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