# set theory simplification #2

• Feb 8th 2010, 10:54 PM
aaronrj
set theory simplification #2
$\displaystyle (A - B) \cup (A\cap B)$

I have the first few steps where the minus is converted to in intersection of A complement B then using associative rule the B complement intersected with B becomes the universe. Not sure if i am on the right track
• Feb 9th 2010, 01:15 AM
bmp05
hey aaronj,

the first step with these questions for me is to do a Venn diagram. In this case, it's a really valuable thing to do, because it shows you what the answer is very quickly.

The next step, depending on the method that the question wants you to use is to show what you already know is the answer- or to put it in a more positive way to check what you found using the Venn diagram.

$\displaystyle (A - B) \cup (A \cap B) \Leftrightarrow ((A - B)\cup A) \cap ((A - B)\cup B)$

Aand then you should recognise both sides of the intersection!
• Feb 9th 2010, 06:54 AM
Plato
Quote:

Originally Posted by aaronrj
$\displaystyle (A - B) \cup (A\cap B)$

$\displaystyle (A - B) \cup (A\cap B)=A\cap(\overline{B}\cup B)=A\cup~ \mathcal{U}=A$