Let f be a function on A onto B. Define a relation E in A by: aEb if and only if f(a)=f(b).

a. Show that E is an equivalence relation on A.

b. Define a function phi on A/E onto B by phi([a]_E)=f(a) (verify that phi([a]_E) = phi([a']_E) if [a]_E = [a']_E)

c. Let j be the function on A onto A/E given by j(a)=[a]_E. Show that phi (dot) j = f.

_ is sub.

Any ideas would be really appreciated! Thanks!