“If X, then Y unless Z” is represented by which of the following formulae in…

Answer: (X ∧ ¬Z) → Y

Explanation: 'If X, then Y unless Z' means that when X holds and Z does not hold, Y must hold. The phrase 'Y unless Z' is equivalent to 'if not Z then Y' (¬Z → Y).

1. Rewrite 'Y unless Z' as an implication: ¬Z → Y.

2. The whole sentence becomes: X → (¬Z → Y).

3. Use the equivalence between nested implications and a conjunction: X → (¬Z → Y) is equivalent to (X ∧ ¬Z) → Y.

Brief notes on the other formulas:

• (X ∧ Y) → ¬Z: This says X and Y together force ¬Z, which is unrelated to the intended conditional about Y unless Z.

• X → (Y ∧ ¬Z): This requires ¬Z whenever X holds, which is stronger than 'unless' and thus incorrect.

• Y → (X ∧ ¬Z): This reverses the implication direction; it constrains X and Z based on Y, not Y based on X and Z.