# Simplifying Sets using Properties

• Oct 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.
• Oct 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: \$\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)\$
• Oct 11th 2011, 11:52 AM
richtea9
Re: Simplifying Sets using Properties
Quote:

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.
• Oct 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 \$\displaystyle (A\cup B)\cap C\$.