Let p and q be the propositions
p : It is below freezing.
q : It is snowing.

Write these propositions using p and q and logical connectives (including negations).

f) Either it is below freezing or it is snowing, but it is not snowing if it is below freezing.

My answer was:
(p ⊕ q) ∧ (¬ q → p)

Because the word 'either' in the beginning of the sentence seems to suggest that we may have one event or another happening, but not both at the same time, which is an exclusive-or case (⊕). And the rest of the answer looks pretty understandable, so I won't dive much into my thinking. The problem is, though, in the book the answer is:
(p V q) A (p→ ¬q), which makes no sense.

Could someone please explain it to me?