# Show whether the set equality is true via subsets

• Feb 4th 2010, 09:21 AM
Runty
Show whether the set equality is true via subsets
Show whether the set equality $(B-A)\cup(C-A)=(B\cup C)-A$ is true, by demonstrating whether each side of the equality is a subset of the other.

I'd be able to do this with membership tables and set identities, but I don't know how to do it in the manner outlined above.
• Feb 4th 2010, 09:30 AM
Plato
$\left( {x \in B \wedge x \notin A} \right) \vee \left( {x \in C \wedge x \notin A} \right) \equiv \left( {x \in B \vee x \in C} \right) \wedge (x \notin A)$