Question: Please use abstract algebra content to solve this problem, thank you. 4. Assume that K is a subgroup of G and N is a normal

Please use abstract algebra content to solve this problem, thank you.

4. Assume that K is a subgroup of G and N is a normal subgroup of G. (a) Prove that KN = {kn|k E K, n E N} is a subgroup of G. (b) Prove that K/(k n N) is isomorphic to KN/N. (This is the Second Isomorphism Theo- rem)

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