Let A = {x, y, z, u} and B = {a, b}. A functi | vedclass

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(D) The total number of functions from set $A$ to set $B$ is given by $|B|^{|A|} = 2^4 = 16$. An onto function (surjective function) means every eleme

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$\frac{7}{8}$

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(D) The total number of functions from set $A$ to set $B$ is given by $|B|^{|A|} = 2^4 = 16$. An onto function (surjective function) means every element in $B$ must have at least one pre-image in $A$. The only functions that are not onto are the constant functions: $f(x) = a$ for all $x \in A$ and $f(x) = b$ for all $x \in A$. There are $2$ such constant functions. Number of onto functions $= 16 - 2 = 14$. Probability of onto function $= \frac{14}{16} = \frac{7}{8}$.

Let $A = \{x, y, z, u\}$ and $B = \{a, b\}$. $A$ function $f: A \rightarrow B$ is selected randomly. The probability that the function is an onto function is

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