# Set Theory (Not too difficult)

gutnedawg

## Homework Statement

describe exactly when
x intersecting (y union z) = (x intersecting y) union z

## The Attempt at a Solution

I just for some reason cannot see this solution and need a shove in the right direction

murmillo
Try drying a Venn diagram. It turns out that the shaded areas are not the same. Then ask yourself what you must do to one or more of the sets so that the shaded areas will be the same.

Homework Helper
or you could use relation
$$x \cap (y \cup z ) = (x \cap y) \cup ( x \cap z)$$

this shoudln't be too difficult to prove if need be

murmillo
Ah, I didn't know that relation. I don't know if the original poster is supposed to know that relation. If that identity can be assumed, then the problem is much easier.

gutnedawg
so lanedance I can just say that if

$$x\cap z = z$$

then the first equality holds?

Homework Helper
yeah, so
$$x\cap z = z \rightarrow$$
$$x \cap (y \cup z ) = (x \cap y) \cup z$$

you should convince yourself through venn diagrams or proof, why this is case

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