Question

The number of surjections from $A=1,2,.....n,n\le 2$, onto B = {a, b} is

• A. ${}^n{P}_2$
• B. $2^n-2$
• C. $2^n-1$
• D. none of these

Answer 1

Answer: (B)

$2^n-2$

A = {1, 2, 3, ........, n}

B = {a, b}

A has n elements.

B has 2 elements.

$\therefore$ No. of surjection is $2^n-2$.