How to translate"If $X$ then $Y$ unless $Z$" to propositional logic.

Question

As the title says, the given sentence is

If $x$ then $y$ unless $z$"

Now according to my learning "If $x$ then $y$" translates to: $x\rightarrow y$. Also according to Kenneth Rosen's book (second paragraph on this page) "$y$ unless $z$" translates to $z\rightarrow y$. Now we have to AND (conjunction) these two. According to 7th formula in table 7 here, this is done as follows:

$(x \rightarrow y)\land (z\rightarrow y) \equiv (x\lor z)\rightarrow y$

However the solution given in the book (not the Kenneth Rosen's book) is

$(x\land \lnot z)\rightarrow y$

Though above seems to be direct verbal translation of the statement "It $x$ then $y$ unless $z$", I am confused how following the rules as given in the book which also sounds correct yields different result.

Answer 1

According to Rosen (7th ed, page 6), “$q$ unless $¬p$” translates : “if $p$, then $q$”.

Thus, for :

"if $x$ then $y$ unless $z$"

assuming a comma : "if $x$ then $y$, unless $z$", we have :

“if $¬z$, then if $x$ then $y$".

Now for the symbols :

$¬z \to (x \to y)$

is equivalent to : $(\lnot z \land x) \to y$ by Exportation, i.e. the tautology :

$((P \land Q) \to R) \Leftrightarrow (P \to (Q \to R))$.

Answer 2

If $x$ then $y$ unless $z$.

The word unless in the original sentence refers to the if at the beginning, that is, the implication (if) holds every time you do not have $z$.

$y$ unless $z$.

In the second sentence, on the other hand, the word unless refers to the $y$ at the beginning, that is, $y$ holds every time you do not have $z$.