Proof of set theory

Question

How would I go about proving this question:

Let A, B, C, D be finite sets with A⊆C and B⊆D. Proof that A×B⊆C×D

Answer 1

Consider an element of the set AxB. It is given as a pair (a,b) where a is an element of A and b is an element of B. Since A is a subset of C we have that a is an element of C and since B is a subset of D we have that b is an element of D. Then by the definition of the set CxD we have that the pair (a,b) belongs to the set CxD. Thus, we showed that AxB is a subset of CxD as desired.