Proving a subset of a cartesion cross product

[ar6]

Homework Statement

A, B, C and D are sets

if A x B is a subset of C x D then A is a subset of C and B is a subset of D.

The Attempt at a Solution

My attempt by contraposition.

Assume A is not a subset of C or B is not a subset of D. There exists an 'a' which is an element of A but is not an element of C and there exists a 'b' that is an element of B but not an element of D. 'a,b' is an element of A x B but 'a,b' is not an element of C x D. Therefore, A x B is not a subset of C X D. Thus, by contraposition, if A x B is a subset of C x D then A is a subset of C and B is a subset of D.

 

[mjsd]

looks ok to me. but I must say I am a bit rusty on this kind of proofs these days. when I have more time, I may return and check it again.

EDIT: on 2nd thought, it still looks good to me