Answer is a) $(X \land \lnot Z)\to Y$
(refer page 6,7 Discrete Math,ed 7, Kenneth H Rosen)
Implication "$P$ implies $Q$" i.e., $(p \to Q)$, where $P$ is Premise and $Q$ is Conclusion, can be equivalently expressed in many ways. And the two equivalent expression relevant to the question are as follows:
- "If $P$ then $Q$"
- "$Q$ unless $\lnot P$"
Both of these are equivalent to the propositional formula $(P \to Q)$,
Now compare "If $X$ then $Y$ unless $Z$" with "$Q$ unless $\lnot P$" , here $(\lnot P = Z)$ so $(P = \lnot Z)$ and $(Q = Y)$
Compare with "if $P$ then $Q$", here $(P = X) , (Q= Y)$
So we get premise $P= X \text{ and } \lnot Z,$ conclusion $Q = Y$
Equivalent propositional formula $(X \land \lnot Z) \to Y$
PS: Someone messaged me that i have taken "If $X$ then ($Y$ unless $Z$)" in above explanation and how to know if we take "(If $X$ then $Y$) unless $Z$" or "If $X$ then ($Y$ unless $Z$)". So let me show that both way gives the same answer.
"(If $X$ then $Y$) unless $Z$" $\equiv (X\to Y)$ unless $Z$
$$\begin{align}
&\equiv \lnot Z \to (X\to Y) \\
&\equiv \lnot Z\to (\lnot X \lor Y) \\
&\equiv Z \lor \lnot X \lor Y \\
&\equiv \lnot (X \land \lnot Z) \lor Y \\
&\equiv (X \land \lnot Z) \to Y
\end{align}$$