Q:

Showing/rewriting logical validity

Hey guys, just a bit confused with this question. I'm not sure exactly how the answer should be given:
Question:
Express the following argument in symbolic form using logical connectives. Be careful to define any notation you introduce:
"1) If I earn some money then I will go for a holiday this summer.
 2) I will either go for a holiday or work this summer.
 3) Therefore, if I don't go for a holiday this summer then I will not have earned any money and will be working"
What I got so far:
let p = "I earn some money"
and q = "I go away for holiday this summer"
and r = "I work this summer"
then by the first statement: $(p\rightarrow q)$
by the second statement: $(q\lor r) \land \lnot(q \land r)$ (exclusive or)
I've yet to fully work out the third statement, but my question is the answer given by three different statements in symbollic form or am I supposed to somehow combine it? 
edit: What would be the third statement? would it be $\lnot(q \rightarrow p)\land r$?

A:

The inclusive vs. exclusive or issue is often one translating natural language to symbolic logic.  You have to decide which "or" the natural language means.  I think in this case I would agree with exclusive, but that is not a mathematical problem.  You have represented the exclusive or correctly.  For the third statement, I would see it as $\lnot q \rightarrow (\lnot p\land r)$, seeing the "then" as grouping the last two phrases.  I'm sure both of the translation decisions can be argued both ways.

