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WAEC Further Mathematics 2025 Question 4

Question 4

Sets and Logic

Consider the statements:
p: the land is fertile
q: the farmer harvests big cassava tubers
r: the sun is harsh
Which of these represents the statement, "If the land is fertile and the sun is not harsh then the farmer harvests big cassava tubers"?

  1. A.(p ∨ ~r) ⇒ q
  2. B.(p ∧ r) ⇒ q
  3. C.(p ∨ r) ⇒ q
  4. D.(p ∧ ~r) ⇒ q
Show the answer and explanation

Answer: D ((p ∧ ~r) ⇒ q)

Explanation

'The land is fertile and the sun is not harsh' is p ∧ ~r; 'if … then the farmer harvests' makes it (p ∧ ~r) ⇒ q.