E-Storeno of into and onto functions
7 May 2007 09:06:52 IST
no of into and onto functions
Let the function be represented by A--> B whr n(A) = n(B)= n
total no of distinct functions from A to B = nn
now no of ways in which yi (
B) is not the image of xi( A) =no of into functions
B) is not the image of xi( A) =no of into functionsLet Ai denotes the event that ith element of B is not the image of any element of A (i.e. A1 is the event in which y1 is nt the image of any x A )
A )thrfore no of ways in which atleast one element of B is not the image of any elemnt in A , (E)= n (A1 
A2 A3 A4 .......An)
A2 A3 A4 .......An)now total no of functions when one element of B doesnt have any pre-image
= no of ways of selecting that elemnt X no of ways in which rest can have thr pre-images
= nC1 (n-1)n
similarly when 2 elemnts doesnt have pre-image then no of functions = nC2 (n-2)n
.....
thus n(E) = nC1 (n-1)n - nC2 (n-2)n + nC3 (n-3)n - ......upto n terms
this will be the no of into fucntions frm A to B
thrfore onto functions = nn - n(E)
Comments (10)
Manasi
Forum Expert
Joined: 1 Dec 2006 11:13:27 IST
Posts: 2108
7 May 2007 10:47:47 IST
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no comments ....seems like no one needs academic articles ????????
10 May 2007 11:54:20 IST
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thanxx a loot didi......very helpful....hey evry1, post ur commentss...
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