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.

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- Feb 18th 2011, 04:15 PMJameDifferent 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. - Feb 18th 2011, 05:48 PMChris L T521
$\displaystyle (C\backslash(A\cup B))^c\neq (A\cup B)\cap C$!!!!!!

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... - Feb 21st 2011, 11:46 AMJame
Thanks so much. Looking at a Venn diagram I was able to see this!