Homomorphisms

Homomorphism

Problem 4:

Let G, G1, and G2 be groups. Let µ1 : G -> G1 and µ2 : G -> G2 be
group homomorphisms. Prove that

µ : G -> G1 Ч G2 defined by :

µ (x) = (µ1 (x), µ2 (x)),     for all x in G,

is a well-defined group homomorphism.