Is H1xH2 a Subgroup of G1 X G2?

[POtment]

Homework Statement

Let G1, G2 be groups with subgroups H1,H2. Show that

[{x1,x2) | x1 element of H1, x2 element of H2} is a subgroup of the direct product of G1 X G2

The Attempt at a Solution

I'm not sure how to begin solving this problem.

 

[Dick]

Show it the usual way you show a set is a subgroup. Show H1xH2 is closed under the group operation, that it has an identity, that it has inverses, etc.