Meaning of "If $X$ then $Y$ unless $Z$"

Question

If $X$ then $Y$ unless $Z$
is represented by which of formula in propositional logic?
I am getting confused between $X\rightarrow \left ( Y\wedge \sim Z \right )$ and $\left ( X \rightarrow Y\right )\wedge \sim Z$.
Is it represented by any other formula than the two?

Answer 1

Neither.

"If X, then Y unless Z" means that if X is true and Z is false, then Y is true; but if X is true and Z is true, then all bets are off.

That is, $$(X\wedge \neg Z)\implies Y.$$

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Actually, there is some ambiguity here, as there often is with natural language: maybe "If X, then Y unless Z" means that if X is true and Z is false, then Y is true, but if X is true and Z is true, then Y is false. Then this would be represented as $$[(X\wedge \neg Z)\implies Y]\wedge [(X\wedge Z)\implies \neg Y],$$ or equivalently $$X\implies (Y\iff \neg Z).$$