Show whether the set equality is true via subsets

**Runty** · February 4th 2010, 08:21 AM

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.

**Plato** · February 4th 2010, 08:30 AM

$\left( {x \in B \wedge x \notin A} \right) \vee \left( {x \in C \wedge x \notin A} \right) \equiv \left( {x \in B \vee x \in C} \right) \wedge (x \notin A)$

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