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Let C be a normal subgroup of the group A and let D be a normal...

Let C be a normal subgroup of the group A and let D be a normal subgroup of the group B.
(a) Prove that C × D is a normal subgroup of A × B
(b) Prove that the map φ : A × B → (A/C) × (B/D) given by φ((m, n)) = (mC, nD) is a group homomorphism.
(c) Use the fundamental homomorphism theorem to prove that (A × B)/(C × D) ∼= (A/C) × (B/D)

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