Let E = { 1,2,3,4} and F = { 1,2} .Then number of onto functions from E to F is

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1.Relation and Function

medium

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

$14$

$16$

$12$

$8$

(IIT-2001)

Solution

(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 $E$ in $F = 2 \times 2 \times 2 \times 2$.
But in two of them all the elements 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$.

Standard 12

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(JEE MAIN-2021)