Let `f : { 1, 2, 3} rarr {a, b, c}` be one-one and onto function given by `f (1) = a`, `f (2) = b` and `f( 3) = c`. Show that there exists a function `g : {a, b, c} rarr { 1, 2, 3}` such that `gof = I_x` and `fog = l_y`. where `X = {1, 2, 3}` and `Y = {a, b, c}`.