Question

1. Let A = {1,2,3,4} and let F be the set of all functions f from A to A. Prove or disprove each of the following statements.

(a)For all functions f, g, h∈F, if f◦g=f◦h then g=h.

(b)For all functions f, g, h∈F, iff◦g=f◦h and f is one-to-one then g=h.

(c) For all functions f, g, h ∈ F , if g ◦ f = h ◦ f then g = h.
(d) For all functions f, g, h ∈ F , if g ◦ f = h ◦ f and f is onto then g = h.

Answer 1