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+2 votes
Find the number of single valued functions from set A to another set B, given that the cardinalities of the sets A and B are $m$ and $n$ respectively.
asked in Set Theory & Algebra by Veteran (39.8k points) 258 1313 1945 | 152 views

2 Answers

+1 vote
Best answer

single valued are the function which has the domain single element map to only one element in Range.

so i tink nare the total number of the Single valued function are there. 

answered by Loyal (3.1k points) 6 17 37
selected by

Yeah, this is the correct definition of a Single valued function.Thanks :-)

+1 vote

A single-valued function is an emphatic term for a mathematical function in the usual sense. That is, each element of the function's domain maps to a single, well-defined element of its range.By default, we always consider function as a single valued function except when clearly mentioned that function is a multi-valued function. 

So, the number of single valued functions from A to B =  number of functions from A to B.

Let an eg.

A ={1,2} ,B={a,b }

1. f(1)=f(2)=a


3.f(1)=a and f(2) =b

4.f(1)=b and f(2) =a

 The total number of single valued functions from set A to another set B =∣ B ∣∣ A ∣​​​​​​​ ​​​​ ​​​​​​​ ​​​​​​= ​​​​​​​nm

The correct answer is nm .

answered by Boss (9.4k points) 4 8 13
edited by
You are absolutely correct with the definition of single valued function but here they are asking about no of functions .

You left out many cases for instance f(1)=f(2)=a,f(3)=b...etc these all instances should be considered !
The solution is corrected now.Thanks, bro.

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