# Math Help - set algebra

1. ## set algebra

using set algebra laws prove the following:

1) (A-B) U (B-A) = (A U B) - (A ∩ B)

2) ((A ∩ B)' U B)' = 0

2. ## Re: set algebra

Start by replacing X - Y by X ∩ Y', then use De Morgan's laws and distributivity of ∩ over U.

3. ## Re: set algebra

Hello, beast!

Here is the second one.
I'll let you supply the reasons.

$[2]\;\;\big[(A \cap B)' \cup B\big]' \:=\:\emptyset$

$\big[(A \cap B)' \cup B\big]'$

. . $=\;\big[(A' \cup B') \cup B\big]'$

. . $=\;\big[A' \cup (B' \cup B)\big]'$

. . $=\; \big[A' \cup U\big]'$

. . $=\;U'$

. . $=\; \emptyset$

4. ## Re: set algebra

1st line - deMorgans?
2nd line - complement law?
3rd line - ???
4th line - ???