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The maximum number of equivalence relations on the set $A=\{1,2,3\}$ is?

(A) 1

(B) 2

(C) 3

(D) 5
Can you answer this question?
 
 

1 Answer

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$R_1=\{(1,1),(2,2),(3,3)\}$
$R_2=\{(1,1),(2,2),(3,3),(1,2),(2,1)\}$
$R_3=\{(1,1),(2,2),(3,3),(1,3),(3,1)\}$
$R_4=\{(1,1),(2,2),(3,3),(2,3),(3,2)\}$
$R_4=\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)\}$
These are the 5 relations on A which are equivalence.
answered May 31, 2013 by rvidyagovindarajan_1
 

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