In: Advanced Math
Let f: X-->Y and g: Y-->Z be arbitrary maps of sets
(a) Show that if f and g are injective then so is the composition g o f
(b) Show that if f and g are surjective then so is the composition g o f
(c) Show that if f and g are bijective then so is the composition g o f and (g o f)^-1 = g ^ -1 o f ^ -1
(d) Show that f: X-->Y is injective iff there exists h: Y-->X such that h o f = id sub x
(e) Show that f: X-->Y is surjective iff there exists h: Y-->X such that f o f = id sub y. The only if requires requires the axiom of choice.
ACCORDING TO MY KNOWLEDGE I PASTED A,B,AND C ANSWERS
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