# Simplifying Sets using Properties

• October 11th 2011, 11:23 AM
richtea9
Simplifying Sets using Properties
First of all, n = intersection because the actual symbol would work for me (Worried)

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.
• October 11th 2011, 11:34 AM
Plato
Re: Simplifying Sets using Properties
Quote:

Originally Posted by richtea9
First of all, n = intersection because the actual symbol would work for me (Worried)
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: $(X\cup Y)\cap X=X$.
So $(A\cup B\cup C)\cap (A\cup B)=(A\cup B)$.
Can you finish?

BTW: Simple LaTeX code,
[TEX](A\cup B\cup C)\cap (A\cup B)[/TEX]
gives $(A\cup B\cup C)\cap (A\cup B)$
• October 11th 2011, 11:52 AM
richtea9
Re: Simplifying Sets using Properties
Quote:

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

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

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.
• October 11th 2011, 12:34 PM
Plato
Re: Simplifying Sets using Properties
Quote:

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 $(A\cup B)\cap C$.