'If X then Y unless Z' is represented by which of the following formulas in propositional logic? ('-' is negation, '/\' ...

Question

'If X then Y unless Z' is represented by which of the following formulas in propositional logic? ('-' is negation, '/\' is conjunction, '->' is implication)

A. (X /\ ~Z) -> Y
B. (X -> Y) /\ (~Z)
C. X -> (Y /\ ~Z)
D. (X /\ ~Z) -> ~Y

Accepted Answer

A. (X /\ ~Z) -> Y 'Unless' means 'if not'. So 'Y unless Z' means 'Y if not Z', i.e., ~Z -> Y, or equivalently Z \/ Y. The full sentence 'If X then Y unless Z' means: if X holds, then Y holds unless Z holds. This translates as: X -> (Z \/ Y), which equals X -> (~Z -> Y), which equals (X /\ ~Z) -> Y by exportation. So option A is correct.

'If X then Y unless Z' is represented by which of the following formulas in propositional logic? ('-' is negation, '/\' is conjunction, '->' is implication) A. (X /\ ~Z) -> Y B. (X -> Y) /\ (~Z) C. X -> (Y /\ ~Z) D. (X /\ ~Z) -> ~Y