Differential Calculus> onto functions...

what is the formula to calculate the no. of onto functions from A to B

prakyath p raj , 15 Years ago

Grade 12

8 Answers

Badiuddin askIITians.ismu Expert

Dear prakyath

If A and B are two sets having m and n elements respectively such that 1≤n≤m then number of onto function from A to B is

∑ (-1)^n-r ⁿC_r r^m r vary from 1 to n

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Last Activity: 15 Years ago

Rehan Vijay Jain

hey can u tell me that in dis ques what shud i take the value of r

Q:- If A= {1,2,3,4} B={4,5,6}, then find he no. of onto functions in this case.

pls tell me as fast it is possible

i need the answer of it too..........

Last Activity: 13 Years ago

Raawi Teza

No of elements of A = 4

No of elements of B = 3

usint this formula ∑ (-1)^n-r ⁿC_r r^m r vary from 1 to n

{[(-1)^(3-1)]*³C₁*1^4} + {[(-1)^(3-2)]*³C₂*2^4{ +{ [(-1)^(3-3)]*³C₃*3^4}

= 1*3*1 + (-1)*3*16 + 1*1*81

= 3-48+81

=36

Last Activity: 13 Years ago

namita

For

set a={a,b,c} and B={m,n}

the number of onto functions by your formula is 6

where as when i try manually it comes 8

according to you what should be the anwer

Last Activity: 12 Years ago

Abishek

If we calculate manually for number of onto functions from A=3 elements to B=2 elements, it comes out to be 6 as from the formula. Can anyone explain the formula.

Last Activity: 11 Years ago

Manas Shukla

If there is set A containing a elements and set B containing b elements, formula to calculate no of onto functions is : {(b to power a)- b}

Last Activity: 8 Years ago

Torun

n^r-nc1(n-1)^r+nc2(n-2)^r-nc3(n-3)^r.....where n=no. of elements in B;r=no. of elements in A. For a function ,f(A to B).Use this one guys ,its perfectttt.

Last Activity: 8 Years ago

ankit singh

Therefore, each element of X has 'n' elements to be chosen from. Therefore, total number of functions will be n×n×n.. m times = n^m. For example: X = {a, b, c} and Y = {4, 5}

Last Activity: 5 Years ago