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Q.
Let $E=\left(\right.1,2,3,4\left.\right)$ and $F=\left(\right.1,2\left.\right)$ . Then the number of onto functions from $E$ to $F$ is
NTA AbhyasNTA Abhyas 2022
Solution:
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 $=2^{4}-2=14$