Hello...

I need real help in these problems...

Please help!

Q1) Prove that if H and K are subgroups of a group G (with operation *), then H intersection K is a subgroup of G.

Q2) Let H = {(1), (1 2)} and K = {(1), (1 2 3), (1 3 2)}. Both H and K are subgroup of S3. Show that HUK is not a subgroup of S3. It follows that a union of subgroup is not necessarily a subgroup.

Thanks in advance!