Set Theory (Not too difficult)

[gutnedawg]

Homework Statement

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

Homework Equations

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.

 

[lanedance]

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?

 

[lanedance]

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