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Write the smallest equivalence relation R on Set A = {1, 2, 3}

Write the smallest equivalence relation R on Set A = {1, 2, 3}

Grade:upto college level

4 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
The smallest equivalence relation on A+{1,2,3} is
A={(1,1)(1,2)(1,3)(2,1)(2,2)(2,3)(3,1)(3,2)(3,3)}
Thanks and Regards
Shaik Aasif
askIITians faculty
Akankshya
46 Points
6 years ago
The smallest equivalence relation on A={1,2,3} is {(1,1), (2,2), (3,3)}..because it is reflexive ,symmetric and transitive at all.
Kishlay
13 Points
6 years ago
The smallest equivalence relation on A={1,2,3} is {(1,1), (2,2), (3,3)}. It is reflexive, symmetric and transitive. Think for a while.... U can take the ordered pair twice to check for these conditions. For eg: Take (1,1), (1,1)... U get reflexive, symmetric as well as transitive. Similarly is the case with (2,2), and (3,3).
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
 
The smallest equivalence relation on A = {1,2,3} is {(1,1), (2,2), (3,3)}
We can this because it is reflexive, symmetric as well as transitive.
 
Thanks and regards,
Kushagra

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