Possible Duplicate:
Whether $P\cap Q$ and $P\cup Q$ are subgroups
How can we prove that the intersection of two subgroups is a subgroup. In more detail, if $G$ is a group and $H_1$ and $H_2$ are subgroups of $G$ then $H_1 \cap H_2$ is a subgroup of $G$.
On the other hand, show by means of an example that $H_1 \cup H_2$ need not be a subgroup of $G$.
