It is given that E & F are subsets of A, so lets say elements of E maps to some elements of co-domain and elements of F maps to some elements of co-domain..
So the incidence of elements of E U F will be same as that of incidence of elements of E U incidence of elements of F
let me take an example and explain..
let A = {1,2,3,4,5} and B = {v,w,x,y,z} where 1 -> v, 2-> w, 3-> x, 4->y, 5->z
and E = {1,2,3}, F= {2,5}
f(E U F) = {v,w,x,z} , f(E) = {v,w,x}, f(F) = {w,z} and f(E) U f(F) = {v,w,x,z},
f(E U F) = f(E) U f(F) = {v,w,x,z}