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.

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

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.

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