Question

3) If G isv group and H is a subgroup of G of
Index 2 then H&G.​

Answer 1

One-step subgroup test

Let G be a group, let H be a nonempty subset of G and assume that for all a and b in H, ab−1 is in H. To prove that H is a subgroup of G we must show that H is associative, has an identity, has an inverse for every element and is closed under the operation.