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WAEC Further Mathematics 2021 Question 31

Question 31

Sets and Logic

Consider the following statements
x: Benita is polite
y: Benita is neat
z: Benita is intelligent
Which of the following symbolizes the statement: 'Benita is neat if and only if she is neither polite nor intelligent'?

  1. A.y ⇔ ~x ∨ z
  2. B.y ⇔ ~x ∨ ~z
  3. C.y ⇔ ~x ∧ ~z
  4. D.y ⇔ ~x ∧ z
Show the answer and explanation

Answer: C (y ⇔ ~x ∧ ~z)

Explanation

'Neither polite nor intelligent' means not polite AND not intelligent: ~x ∧ ~z. So the statement is y ⇔ (~x ∧ ~z).