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## Homework Statement

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Sorry that I wasn't able to fit everything in the title. I got 2/3 on this on my quiz, and am wondering what I did wrong, or could have done better. Thanks in advance.

Show that if A ⊆ B and C ⊆ D, then A X C ⊆ B X D

## Homework Equations

## The Attempt at a Solution

For a given value x, if A ⊆ B, then x ∈ A

**and**x ∈ B.

For a given value x, if C ⊆ D, then x i∈ C

**and**x ∈ D.

Cartesian product of (A, C) means that all ordered pairs, (a, c) are included.

Cartesian product of (B, D) means that all ordered pairs, (b, d) are included.

A X C ⊆ B X D