GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
102 views
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 (32.8k points)   | 102 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)  
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

2.f(1)=f(2)=b

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 ago by Active (1.7k points)  
edited ago 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.


Top Users Aug 2017
  1. ABKUNDAN

    4654 Points

  2. Bikram

    4012 Points

  3. akash.dinkar12

    3136 Points

  4. rahul sharma 5

    2832 Points

  5. manu00x

    2644 Points

  6. makhdoom ghaya

    2370 Points

  7. just_bhavana

    2040 Points

  8. Tesla!

    1742 Points

  9. pawan kumarln

    1574 Points

  10. learner_geek

    1554 Points


24,864 questions
31,941 answers
74,060 comments
30,062 users