Question

Let $E=\left\{1,2,3,4\right\}$ and $F=\left\{1,2\right\}$. Then the number of onto functions from $E$ to $F$is?

Answer 1

Determine the number of onto functions:

Suppose $S$ is a set with $\left\{\overline{)f}f:E\to F\right\}$. Then, the total number of functions for $\left|S\right|={\left|F\right|}^{\left|E\right|}$.

From the given sets we get:

The total number of functions for $E$ and $F=2^4=16$.

Now, the total number of into functions for $E$ and $F$ is $2$,

Since the Total number of onto functions is equal to the difference of into function from the total number of functions.

$\therefore 16-2=14$

Hence, the total number of onto functions are $14$.