Let E = { 1, 2, 3, 4 } and F = { 1, 2 } . Th | vedclass

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(A) The total number of functions from a set $E$ with $n$ elements to a set $F$ with $m$ elements is $m^n$. Here,$n = |E| = 4$ and $m = |F| = 2$. So,t

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$14$

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(A) The total number of functions from a set $E$ with $n$ elements to a set $F$ with $m$ elements is $m^n$. Here,$n = |E| = 4$ and $m = |F| = 2$. So,the total number of functions is $2^4 = 16$. An onto function (surjective function) means every element in the codomain $F$ must have at least one pre-image in the domain $E$. The only functions that are not onto are those where all elements of $E$ map to either ${1}$ or ${2}$. There are exactly $2$ such constant functions: $f(x) = 1$ for all $x \in E$ and $f(x) = 2$ for all $x \in E$. Therefore,the number of onto functions is $16 - 2 = 14$.

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

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