question_answer 67)

Let S = {a, b, c} and T = {1, 2, 3}. Find F–1 of the following functions F from S to T, it is exists. (i) F = {a, 3}, (b, 2), (c, 1)} (ii) F = {(a, 2), (b, 1), (c,1)}  

Answer:

. (i) F : S  T is defined as       F = {(a, 3), (b, 2), (c, 3)}        so F is an onto function.       As RF = T, to F is an onto function.       Also different elements of S have different F-images, so F is one-one function.        is both one-one onto function        is defined as       .       (ii) is defined as       F?1 = {(a, 2), (b, 1), (c, 1)}       Clearly F(b) = 1 and F(a) = 1       is not one-one.       Hence F is not invertible.