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Question: let g1 g2 be a homomorphism between...

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Let ϕ : G1 → G2 be a homomorphism between two groups. Let K be a subgroup of G2. Prove that ϕ −1 (K) is a subgroup of G1. Note: ϕ −1 (K) = {x ∈ G1 | ϕ(x) ∈ K} is the inverse image (or preimage) of K. x ∈ ϕ −1 (K) iff ϕ(x) ∈ K

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