Question: Let A, B and G be groups. Show: (a) Every normal subgroup of A is a normal subgroup of A B. (b) From U A

Let A, B and G be groups. Show:

(a) Every normal subgroup of A is a normal subgroup of A B.

(b) From U A B it does not necessarily follow that U = (U A) (U B).

Definition of a subgroup: N is a subgroup of G, if Nx = xN N = x-1Nx for all x in G.

Please try to explain it to me simply and in detail, because i would really like to understand it. Thank you in advance!!

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