How Can Set Identities Help with Cartesian Product Homework?

[ainster31]

Homework Statement

Homework Equations

I have to use these set identities:

The Attempt at a Solution

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

 

[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.