The set is (A union B) intersect C.
I was wondering if there was another way to write this that is not
(A intersect C) union (B intersect C)
I was thinking complement of (C \ (A union B))
Thank you for your help.
$\displaystyle (C\backslash(A\cup B))^c\neq (A\cup B)\cap C$!!!!!!
You could say
$\displaystyle \begin{aligned}(A\cup B)\cap C &= [(A\cap C)\backslash B] \cup (A\cap B\cap C)\cup[(B\cap C)\backslash A]\\ &=[(A\cap C)\backslash B]\cup (B\cap C) \\ &= (A\cap C)\cup [(B\cap C)\backslash A]\\ &= C\cap(C\backslash(A\cup B))\\ &= (A\cap C)\cup(B\cap C)\\ &= \ldots\end{aligned}$
There are many different ways of saying the same thing...