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
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