A = {1,2,3}, B = {4,5,6}, C = {7,8,9,10} define the functions f :A→C and g:B→C by f(1) = 7, f(2) = 9, f(3) = 7, g(4) = 10, g(5)=7 ,g(6)=9 Does there exist a function h : A → B such that g ◦ h = f ?   Does there exist a function k : B → A such that f ◦ k = g? Justify your answers.

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