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

###### Question details

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