Assignment:
Let G sub1 and G sub 2 be groups, with subgroups H sub 1 and H sub 2, respectivetly. Show that {(x sub 1, x sub 2) | H sub 1 is an element of H sub 1, x sub 2 is an element of H sub 2} is a subgroup of the direct product G sub 1 x G sub 2.
Provide complete and step by step solution for the question and show calculations and use formulas.