How to understand such a complex event $\left((a\cap\grave{b})\cup(b\cap\grave{a})\right)$ in probability?

Question

What is the meaning of the event $\left((a\cap\grave{b})\cup(b\cap\grave{a})\right)$ in probability?

Answer 1

Looking at the first part $a\cap b'$ we have members of $a$ not in $b$. For the second part $b\cap a'$ we have members of $b$ not in $a$. When we union these two pieces we're asking for the members of the two exclusive groups (exclusive $a$ members on the left, exclusive $b$ members on the right if we're thinking in terms of a Venn Diagram).