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Prove this statement: Let ϕ : A1 → A2 be a homomorphism and let N =...

Prove this statement: Let ϕ : A1 → A2 be a homomorphism and let N = ker ϕ. Then A1/N is isomorphic to ϕ(A1). Further ψ : A1/N → ϕ(A1) defined by ψ(aN) = ϕ(a) is an isomorphism.

You must use the following elements to prove:

- well-definedness

- one-to-one

- onto

- homomorphism

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