Let G be a group and let H and K be subgroups of G. Prove that the intersection of H and K, H n K = {x € G |x E H and x E K} is a subgroup of G. Give an example to show that the union H U K = {x E H or x E K} need not be a subgroup of G. (a) Does K 4H and H 4G imply K 4 G ? (b) If K C H, does K 4G and H 4 G imply K 4H ?

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