Question

Let $E=\left\{1,2,3,4\right\}$, $F=\left\{a,b\right\}$ then the number of onto function from $E$ to $F$ is?

• A. $14$
• B. $16$
• C. $12$
• D. $32$

Answer 1

The correct option is A

$14$

Explanation for correct option:

Finding the number of onto functions:

$E=\left\{1,2,3,4\right\}$

So, number of elements present in the set $E$ is $\left|E\right|=4$.

$F=\left\{a,b\right\}$

So, number of elements present in the set $F$ is $\left|F\right|=2$.

The total number of functions from $E$ to $F$ is

$$\begin{gathered} {\left|F\right|}^{\left|E\right|}=2^4 \\ =16 \end{gathered}$$

Hence, The total number of functions from $E$ to $F$ is $16$

The number of functions that do not have $a$ as the range is equal to $1$

Subtract those functions which do not have $b$as the range is equal to $1$

Therefore the number of onto functions from $E$ to $F$

$$\begin{gathered} 16–1-1=16-2 \\ =14 \end{gathered}$$

Hence, the correct answer is option (A).