If A = {x mid x in N, x leq 5} and B = {x mid | vedclass

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(D) Given sets are $A = \{1, 2, 3, 4, 5\}$ and $B = \{x \in Z \mid x^{2} - 5x + 6 = 0\}$.Solving the quadratic equation $x^{2} - 5x + 6 = 0$,we get $(

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$30$

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(D) Given sets are $A = \{1, 2, 3, 4, 5\}$ and $B = \{x \in Z \mid x^{2} - 5x + 6 = 0\}$.Solving the quadratic equation $x^{2} - 5x + 6 = 0$,we get $(x - 2)(x - 3) = 0$,so $x = 2$ or $x = 3$.Thus,$B = \{2, 3\}$.The number of elements in $A$ is $n(A) = 5$ and the number of elements in $B$ is $n(B) = 2$.The number of onto (surjective) functions from a set with $n$ elements to a set with $m$ elements is given by the formula $\sum_{k=0}^{m} (-1)^{m-k} \binom{m}{k} k^{n}$.For $n = 5$ and $m = 2$,the number of onto functions is $2^{n} - 2 = 2^{5} - 2$.$2^{5} - 2 = 32 - 2 = 30$.Therefore,the number of onto functions is $30$.

If $A = \{x \mid x \in N, x \leq 5\}$ and $B = \{x \mid x \in Z, x^{2} - 5x + 6 = 0\}$,then the number of onto functions from $A$ to $B$ is:

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