Can anyone help me with these questions? I have no idea how to get even started.
(Monotony) Let A, B and C be nonempty sets with total orders ≺A, ≺B and ≺C, as well as f: A → B and g: B → C. Prove or disprove the following statements.
a) If f is strictly antitone and g is strictly isotone, then g ◦ f is strictly antitone.
b) If f and g are isotone, then g ◦ f is strictly isotone.
c) If f isotone and g are injective, then g ◦ f is injective.