# Group with subgroups proof

#### kathrynag

1. Homework Statement

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

2. Homework Equations

3. 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.

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#### 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 $$a^{-1} \epsilon K$$.

that makes sense

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