# Proving a set identity

1. Feb 7, 2014

### ainster31

1. The problem statement, all variables and given/known data

2. Relevant equations

I have to use these set identities:

3. The attempt at a solution

Pretty sure this is impossible because there's no identity for the Cartesian product.

2. Feb 7, 2014

### kduna

Just go at it the old fashion way.

Suppose (a, d) $\in$ A X (B $\cup$ C). Then a $\in$ A. Also d $\in$ B or d $\in$ C. So (a,d) $\in$ (A X B) or (a,d) $\in$ (A X C).

Thus (a,d) $\in$ (A X B) $\cup$ (A X C).

Therefore A X (B $\cup$ C) $\subseteq$ (A X B) $\cup$ (A X C).

Proving the subset goes the other way follows similarly.