# Thread: Set Operations

1. ## Set Operations

Hi All, hope I have the correct forum first of all.

I have the following set expression:

$\displaystyle (Y \cap X) \cap (X \cap Y)$

I want to simplify the expression further. However I need to show full workings out. Could I simply just use the idempotence operation so it would become the following?

$\displaystyle Y \cap X$

2. ## Re: Set Operations

Originally Posted by richtea9
I have the following set expression:
$\displaystyle (Y \cap X) \cap (X \cap Y)$
$\displaystyle Y \cap X$
Well for all sets $\displaystyle A$ we have $\displaystyle A\cap A=A$.
Also $\displaystyle (Y\cap X)=(X\cap Y)$.
What more do you need?

3. ## Re: Set Operations

Originally Posted by Plato
Well for all sets $\displaystyle A$ we have $\displaystyle A\cap A=A$.
Also $\displaystyle (Y\cap X)=(X\cap Y)$.
What more do you need?
So the correct operation is idempotence? I wouldn't first have to use distributivity or commutativity?

Just to note: I have simplified this expression from another one.

4. ## Re: Set Operations

Originally Posted by richtea9
So the correct operation is idempotence? I wouldn't first have to use distributivity or commutativity? Just to note: I have simplified this expression from another one.
I think only your instructor can comment of the level of rigor required of you.

5. ## Re: Set Operations

"Idempotence" is not an operation- it is a property.

What definition of $\displaystyle A\cap B$ are you using that $\displaystyle A\cap B= B \cap A$ isn't immediate?