**If are subgroups of a group G then is a subgroup of G.**

**False**

**Discussion:** If one of the groups is normal then the above assertion would be true. Suppose then consider the elements and both of which are members of the set of . If is a group then their product will also be a member of . That is .

Suppose one of the subgroups, say is normal then or there exists such that . Hence and this element definitely belongs to as . Existence of identity and inverse are easy to prove.

Google