Let g : A -> B and f : B -> C be functions.

Show that if f and g are injective, then f o g is injective.

Show that if f and g are surjective, then f o g is surjective.

i don't know how to proove it

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- Oct 20th 2009, 11:33 AMneelpatel89Prooving surjective and injective functions
Let g : A -> B and f : B -> C be functions.

Show that if f and g are injective, then f o g is injective.

Show that if f and g are surjective, then f o g is surjective.

i don't know how to proove it - Oct 20th 2009, 02:45 PMp00ndawg
b.

since f is surjective, rng f = C. That is, for any c C, there exists b B such that f(b) = c. Now since g is surjective, there exists an a A such that g(a) = b. but then (f o g)(a) = f(g(a)) = f(b) = c, so

f o g is surjective. - Oct 20th 2009, 02:51 PMredsoxfan325