Is H ∩ K a Subgroup of G with Subgroups H and K?

[kathrynag]

Homework Statement

Let G be a group with subgroups H and K. Prove HintersectK is a subgroup.

Homework Equations

The Attempt at a Solution

G is a group with subgroups H and K. Then H and K are closed, have identity elements in G and have inverses.
HintersectK is a subgroup because H and K must satisfy the same properties of G.

 

[NJOsment]

let a,b \epsilon H and a,b \epsilon K.Then a*b \epsilon H and a*b \epsilon K.Let a \epsilon H and a \epsilon K.Then a^{-1} \epsilon H and a^{-1} \epsilon K.

 

[kathrynag]

that makes sense