Without using Lemma 3.9 prove that: (a) Every homomorphic image of a divisible abelian group is divisible.

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Without using Lemma 3.9 prove that:

(a) Every homomorphic image of a divisible abelian group is divisible.

(b) Every direct summand of a divisible abelian group is divisible.

(c) A direct sum of divisible abelian groups is divisible.

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