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A function is defined by mapping f : A → B such that A contains m elements and B contains n elements and 1≤n≤m then number of onto functions are ________

A function is defined by mapping f : A → B such that A contains m elements and B contains n elements and 1≤n≤m then number of onto functions are ________ Correct Answer r=1∑r=n nCr (-1)n-r rm

The number of onto function is equal tpo the coffecient of xm in m!(ex – 1)n.

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Consider the set of all functions f: {0,1, … ,2014} → {0,1, … ,2014} such that f(f(i))=I, for all 0 ≤ i ≤ 2014. Consider the following statements: P. For each such function it must be the case that for every i, f(i) = i Q. For each such function it must be the case that for some i, f(i) = i R. Each such function must be onto. Which one of the following is CORRECT?
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3. Supervisory functions
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