Textbook problem: Use unions, intersections, and complements to express the set of elements that are in at least one of the sets $A$ or $B$, where $A$ and $B$ are subsets of the set $\Omega$.
My solution: Using juxtaposition to denote intersections my solution is $AB^c \, \cup \, BA^c \, \cup \, AB$ because I think it's the set of elements in $A$ but not $B$, in $B$ but not $A$, or in both $A$ and $B$.
Textbook solution: $(A\,\cup B)\,\cap\,(A\,\cap\,B)^c$ which I believe to be equivalent to $AB^c \, \cup \, BA^c$ using de Morgan's laws.
Question: Is the textbook solution a mistake or am I misunderstanding the problem?
Note that this is not for a course; I'm self-studying. This is an appendix problem on set notation and operations from an introduction to probability textbook. This particular appendix is preliminary material for the text proper.