2.2 Set Operations: Discrete Mathematics and its application

modzz
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page.130 Ex.20

Ex.20
Show that if A and B are sets, then (A\capB) \bigcup (A\capB) = A.

how do u solve this?



The Attempt at a Solution

 
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You can't. It's false.
 
modzz:

did you possibly mis-type? Do you mean to show

<br /> (A \cap B) \cup (A - B) = A<br />
 
modzz said:
page.130 Ex.20

Ex.20
Show that if A and B are sets, then (A\capB) \bigcup (A\capB) = A.

how do u solve this?



The Attempt at a Solution


I'm having trouble with this question as well. The second B has a line above it if that means anything. Please help me.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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