Let G be the cyclic group Z_4 under addition, of integers modulo 4. Let H be the subgroup of multiples of 2, {0,2}. Write out the two distinct cosets of H. One is 0+H=H. The other is some g+H. Then write out the addition table for the quotient group G/H consisting of those two cosets. The sum of a+H and b+H will be a+b+H.

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