# Different way to express this set

• February 18th 2011, 04:15 PM
Jame
Different way to express this set
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.
• February 18th 2011, 05:48 PM
Chris L T521
Quote:

Originally Posted by Jame
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.

$(C\backslash(A\cup B))^c\neq (A\cup B)\cap C$!!!!!!

You could say

\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...
• February 21st 2011, 11:46 AM
Jame
Thanks so much. Looking at a Venn diagram I was able to see this!