Question

The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is

Options

• 14

• 12

• 2

• 15

Answer 1

14

Explanation:

If A and B are two sets having m and n elements such that 1 ≤ n ≤ m

Then, no. of surjection = `sum_(r = 1)^n (-1)^(n - n) C_rr^m`

Number of surjection from A to B

= `sum_(r = 1)^2 (-1)^(2 - 2) Cr(r)^4`

= `(-1)^(2 - 12)C_1(1)^4 + (-1)^(2 - 22) C_2(2)^4 = - 2 + 16`

= 14