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  3. let f: x-->y and g: y-->z be arbitrary maps

Let f: X-->Y and g: Y-->Z be arbitrary maps of sets (a) Show that if f...

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Advance 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 thecomposition g o f

(b) Show that if f and g are surjective then so is thecomposition g o f

(c) Show that if f and g are bijective then so is thecomposition 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 requiresthe axiom of choice.

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