Let VE GH be a homomorphism, and set K = ker(#). Let of be the canonical homomorphism $ G G/K defined by $(x) = IK. a) Show that v(x) = v(y) if and only if o(x) = $(y). (hint: the First Isomorphism Theorem should be helpful here.) b) Show that the size of the pre-image (x) is the same for all r. What is this size equal to? (hint: consider the pre-images of o.)