If you let G and H be two groups and consider the product group G x H and let K be the subset of G x H given by K ={(g,e_H) | g ∈ G}. How would you prove that (G x H) / K is isomorphic to H using the 1st isomorphism theorem? I was given a hint to start with a map f: G × H -> H that sends (g, h) to h

If you let G and H be two groups and consider the product group G x H and let K be the subset of G x H given by

K ={(g,e_H) | g ∈ G}. How would you prove that (G x H) / K is isomorphic to H using the 1st isomorphism theorem?

I was given a hint to start with a map f: G × H -> H that sends (g, h) to h