How many onto (or surjective) functions are there from an n-element (n >= 2) set to a 2-element set?
(A)
2(2n – 2)
(B)
2n – 2
(C)
2n – 1
(D)
2n
Answer: (B)
Explanation:
Total possible number of functions is 2n.
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if every element y in Y has a corresponding element x in X such that f(x) = y
There are total 2 functions out of 2n that are NOT onto: one that maps to all 1s and other that maps to all 2s.
Therefore total number of onto functions is 2n – 2.
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