Q. 43.7( 3 Votes )

Let A = {a, b c},

Answer :

Given, A = {a, b, c}, B = {u, v, w} and


f = A B and g: B A defined by


f = {(a, v), (b, u), (c, w)} and


g = {(u, b), (v, a), (w, c)}


For both f and g, different elements of domain have different


images


f and g are one – one


Again, for each element in co – domain of f and g, there is a pre – image in the domain


f and g are onto


Thus, f and g are bijective.


Now,


gof = {(a, a), (b, b), (c, c.)} and


fog = {(u, u), (v, v), (w, w)}


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