# Thread: Simplifying Sets using Properties

1. ## Simplifying Sets using Properties

First of all, n = intersection because the actual symbol would work for me

Code:
(A U B U C U D) n (A U B U C) n (A U B) n C
I need to simplify the set expression given above. I think the answer is (A U B) n C? Maybe even A n C?

Maybe the above is correct but I want to know how to show the stages of simplifying it. For example, by commutativity, associativity and idempotence.

Any help would be great, thanks.

2. ## Re: Simplifying Sets using Properties

Originally Posted by richtea9
First of all, n = intersection because the actual symbol would work for me
Code:
(A U B U C U D) n (A U B U C) n (A U B) n C
I need to simplify the set expression given above. I think the answer is (A U B) n C? Maybe even A n C?
This is always true: $\displaystyle (X\cup Y)\cap X=X$.
So $\displaystyle (A\cup B\cup C)\cap (A\cup B)=(A\cup B)$.
Can you finish?

BTW: Simple LaTeX code,
[TEX](A\cup B\cup C)\cap (A\cup B)[/TEX]
gives $\displaystyle (A\cup B\cup C)\cap (A\cup B)$

3. ## Re: Simplifying Sets using Properties

Originally Posted by Plato
This is always true: $\displaystyle (X\cup Y)\cap X=X$.
So $\displaystyle (A\cup B\cup C)\cap (A\cup B)=(A\cup B)$.
Can you finish?

BTW: Simple LaTeX code,
[TEX](A\cup B\cup C)\cap (A\cup B)[/TEX]
gives $\displaystyle (A\cup B\cup C)\cap (A\cup B)$
Hi

Thanks for the reply, am I right by thinking its just A? (Looking at the first expression you gave.) If so I don't see how this would show the same as the set expression I gave on a venn diagram.

4. ## Re: Simplifying Sets using Properties

Originally Posted by richtea9
am I right by thinking its just A? (Looking at the first expression you gave.) If so I don't see how this would show the same as the set expression I gave on a venn diagram.
The answer is $\displaystyle (A\cup B)\cap C$.

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