Question

How can you find out many relations are possible between any two functions?

Answer 1

it depends on the size of the domain and codomain

Answer 2

lets say you have a function f : A->B , so A and B are your domain and codomain

Answer 3

the number of functions is |B| ^|A| , this only makes sense for finite sets A and B

Answer 4

|B| means the size of set B

Answer 5

here is an example :
lets say A = { 1,2} and B = {a,b}

the total number of functions
{ {(1,a) (2,a)}, {(1,a) (2,b)}, {(1,b) (2,a)} {(1,b) (2,b)} }
there are 2^2 number of functions

Answer 6

now without loss of information, we can concentrate only on the y values of (x,y) since the x values are always the same (here x=1 then x = 2 , etc )
so for our example we have aa ab ba and bb correspond to the functions

How about A = { 1,2} and B = { a,b,c}
now we have
aa, ab, ac, ba, bb, bc, ca, cb, cc
notice there are 3^2 possible functions.
that is also equal to |B| ^ |A|

Also as a reminder
aa = (1,a) , (2,a)
bc = (1,b) (2,c)

Answer 7

also keep in mind that a function is a special type of relation, where the x values do not repeat

Answer 8

@perl uts function , it suppose to be 1-1 , and onto

Answer 9

the total number of functions { {(1,a) (2,a)}, {(1,a) (2,b)}, {(1,b) (2,a)} {(1,b) (2,b)} }
it means its not function

Answer 10

he asked how many functions are possible between two sets ,

Answer 11

yep it has :)

Answer 12

those are separate functions

Answer 13

(1,a) ( 2,a) , thats one function
(1,a) (2,b) thats another function

Answer 14

1-1 and onto was not stipulated in the question

Answer 15

ohh lolz ok i got u nw :)

Answer 16

thats why i seperated the elements of the set with braces { }