question_answer 66)

Find the number of all onto functions from the set {1, 2, 3, 4 ….. n} to itself. 

Answer:

Given S = {1, 2, 3, 4, ?.. n}       Let f : S  S be an onto function       Since Rf = S, therefore f is also one-one. Thus f is both one-one onto function. Therefore number of functions is equal to number of arrangement of n numbers taken all at a time i.e.,       So, there are  onto functions from set {1,2, 3, 4, ?., n} to itself.