# The total number of onto functions from the set A = (1, 2, 3, 4, 5) to the set B = {x, y} is

Question:

The total number of onto functions from the set A = (1, 2, 3, 4, 5) to the set B = {xy} is _________.

Solution:

Given: $f: A \rightarrow B$ where $A=\{1,2,3,4,5\}$ and $B=\{x, y\}$

Number of elements in = 5
Number of elements in = 2

Each Element of A have 2 options to form an image.

Thus, Total number of functions that can be formed = 2 × 2 × 2 × 2 × 2 = 32

Number of functions having only one image i.e., {x} = 1
Number of functions having only one image i.e., {y} = 1

Thus, Number of onto functions that can be formed = 32 − 1 − 1 = 30

​Hence, the total number of onto functions from the set A = {1, 2, 3, 4, 5} to the set B = {xy} is 30.