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Proof for sets

I have quite a few of these homework questions as we're studying sets at the moment.

I was wondering if anyone would be kind enough to do one for me to give me an idea as to how to go about them?

Thank you :smile:

Let A, B and C be sets.

Prove that (A u B) n C = (A n C) u (B n C)

u: union
n: intersection

(edited 13 years ago)

Reply 1

Oh I Really Don't Care

Original post by nuodai

Imagine A,B,C are numbers rather than sets. How would you arrange + and × in that expression to make it true? So think about how these relate to

\cup

and

\cap

Quite useless advice. Union distributes over intersection, intersection distributes over union [I seem to recall addition is not distributive over multiplication - sounds like that could be so].

Reply 2

nuodai

Original post by DeanK22

Quite useless advice. Union distributes over intersection, intersection distributes over union [I seem to recall addition is not distributive over multiplication - sounds like that could be so].

I can't say I appreciate your sarcasm, but fair enough. It's not useless advice if only one solution is required, in which case I'd have thought the +,× analogy makes it easier to understand.

EDIT: Oh, the OP's updated the post. At first it had ? signs instead of the union/intersections, so I assumed it was plugging in