Question

Show that intersection of any two subgroup of a group G is aslo a sub group of G

Answer 1

Answer:

In more detail, if G is a group and H1, H2 are subgroups of G then H1∩H2 is a subgroup of G. Next, give an example of a particular group G (any one you like), and two different subgroups H1, H2 of G , compute the intersection H1∩H2 , and verify it is indeed a subgroup.

Finally, give three examples showing that H1∪H2 need not be a subgroup of G .