I think it is legal. I remember asking my professor the same question, and the answer was that it is legal, you just solve it from left to right one operation at a time.
found myself confronted with an interesting problem that i was not 100% sure on,
is:
x1 and (not)x2 or x3
a Boolean expression? (notice the lack of parenthesis around x1 and x2 or x2 and x3)
i believe not since there are "no parenthesis" around one of the expressions.
(im not asking how to solve it or anything, just if its valid, at first i thought it was so i continued on to solve it using proofs but then i realized the lack of parentheses created a problem.
thanks.
-Vindicated