Let A = {1, 2, 3, 4} and B = {a, b} be two sets. Write total number of onto functions from A to B.

Question

Philoid · Accepted Answer

Formula:-

(I)A function is onto function or surjection if

Range (f)=co-domain(f)

(II)if A and B are two non-empty finite sets containing m and n

(i) Number of function from A to B = n^m

(ii) Number of one–one function from A to B

(iii) Number of one-one and onto function from A to B

(iv) Number of onto function from A to B=

Given:-

(i)A = {1, 2, 3, 4}=4

(ii)B = {a, b}=2

Using formula (iv)

Number of onto function from A to B=

Where m=4,n=2

=-2+16=14