Set Operations

**richtea9** · November 4th 2011, 09:33 AM

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

I have the following set expression:

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

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?

$Y \cap X$

**Plato** · November 4th 2011, 09:41 AM

Originally Posted by richtea9

I have the following set expression:
$(Y \cap X) \cap (X \cap Y)$
$Y \cap X$

Well for all sets $A$ we have $A\cap A=A$ .
Also $(Y\cap X)=(X\cap Y)$ .
What more do you need?

**richtea9** · November 4th 2011, 09:48 AM

Originally Posted by Plato

Well for all sets $A$ we have $A\cap A=A$ .
Also $(Y\cap X)=(X\cap Y)$ .
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.

**Plato** · November 4th 2011, 09:57 AM

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.

**HallsofIvy** · November 6th 2011, 03:55 AM

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

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

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