Question

If $A=\{x|x\in N,x\le 5\},$$B=\{x|x\in Z,x^2-5x+6=0\},$ then the number of onto functions from $A$ to $B$ is

• A. 30
• B. 2
• C. 32
• D. 23

Answer 1

The correct option is A 30

$A=\{1,2,3,4,5\Rightarrow n(A)=5\}$
$B=\{2,3\Rightarrow n(B)=2\}$
Total number of functions$=2^n=2^5=32$
Number of onto functions $=2^n-2=2^5-2=30.$