A function f: Z Z S Z is defined by f(x, y) = x + y. a. Prove that f is a homomorphism from the group 3Z Z, +4 (where + means componentwise addition) to the group 3Z, +4. b. Find the kernel K.

i\ t' \ te.( Y uOL \i uf rl> F L* \,*Ct(ri t-Y^\( Lr Lr'\ \- ")i- t-t\ / I r,e,,;) L" ---...