Question

In group g={0,1,2,3,4,5} under addition modulo 6,a subgroup is

Answer 1

Take H = { 0, 2, 4}

We need to prove that H is a subgroup of G.
Conditions for subgroup:
1. The identity element of H belongs to H
2. For any two elements a, b belong to H
implies a*(b inverse) belong to H

It is easy to prove that H it self is a
Group under addition modulo 6 which I have done in the attachment.

It is enough that the above two conditions of subgroup will automatically satisfy.