Discussion Forum

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

Answer:

Explanation:

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

 $1\leq n \leq m=\sum_{r=1}^n (-1)^{n-r}$  $^{n}C_{r}r^{m}$

 Number of surjection from A to B

 $\sum_{r=1}^n(-1)^{2-r}$   $^{2}a_{r}(r)^{4}$

 =  $(-1)^{2-1} .{^{2}C_{1}}(1)^{4}+(-1)^{2-2}. {^{2}C_{2}}(2)^{4}=-2+16$

   =14