If for a function f:A-B such that if mod A=m& mod B=n then number of onto functions is n^m-(n1)(n-1)^m+(n2)(n-2)^m-(n3)(n-3)^m+.....for m greater than or equal to n Sir please explain what is (n1),(n2)...with an example.Thank you.
Asked by Gayathri devi | 9th Nov, 2010, 12:00: AM
In the function f:A-B such that if mod A=m& mod B=n must be number of elements of A and B and not modulus.
Also each element of set A can be mapped to any of the elemements of the set B i.e n.n.n.....till m times so total mappings are nm Now if all the elements are mapped to n1 or to n2 or to n3 and so on ... (the element in set B) then the mapping cannot be onto so the condition in which all elements are mapped to n1 or n2 or n3 etc must be subtracted from the total mappings.
Here n1, n2 etc are the i ,2,3 and 4 th and so on elements of set B.
Hope it clarifies your doubt
Answered by | 18th Nov, 2010, 10:45: AM
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