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18 votes
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Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is

  1. $n$
  2. $n^2$
  3. $1$
  4. $n+1$

5 Answers

Best answer
23 votes
23 votes
Answer is $B$.

The largest equivalence relation will be when every element is related to every other element. So, $n \times n = n^2$ possible ordered pairs.
edited by
4 votes
4 votes

∣A∣ =n

Largest equivalence relation on set A = A ⨉ A

And the Number of elements in the Largest equivalence relation on set A = ∣A ⨉ A∣ = n^2

The correct answer is (B) n^2

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|(1,1)                         |   

|  (2,2)                       |

|     ……..                  |

|          ………           |

|                        (n,n)|

 

on the above matrix of n*n 

largest Reflaxive Relation will be : n*n (must be diagonal + non_diagonal present for the purpose of largest)

largest symmetric Relation will be : n*n (diagonal + non_diagonal present for the purpose of largest)

largest Transitive Relation will be : n*n (diagonal + non_diagonal present for the purpose of largest)

 

then conclusion should be for equivalance rel.  ref , symm , trans 

largest equi. rel . = N*N

 

Please  correct if i am wrong 

Thank you !!

  

 

 

Answer:

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