Question

Let $E=(1,2,3,4)$ and $F=(1,2)$ . Then the number of onto functions from $E$ to $F$ is

• A. $14$
• B. $16$
• C. $12$
• D. $8$

Answer 1

Answer: (A)

The number of ways to give image to each element of $E$ in $F$ is $2$ .
$\therefore$ the total number of ways to give images to the elements of $EinF=2\times 2\times 2\times 2$
But in two of them all the clements of E have the same image $1$ or the same image $2$ (the mapping being into in these two cases).
$\therefore$ the number of onto functions $=2^4-2=14$