1. ## Subset problem

This is my question:
Prove if $A \subset (B \cup C)$, then A= $(A\cap B) \cup (A \cap C)$.

I started my proof like this:
Let $x \epsilon (B\cup C).$ Then this means that $x \epsilon B and x \epsilon C.$

Im stuck right here.

2. I think you meant x is an element of B OR x is an element of C.

try this...

A is a subset of (B union C) means that

A = A intersect (B union C)

then apply the distributive law... (thanks grandad ;p)

3. Hello everyone
Originally Posted by billa
...then apply de morgan's law
I'm sure billa means the Distributive Law.