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The maximum number of equivalence relations on the set A = {1, 2, 3} areA. 1B. 2C. 3D. 5 |
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Answer» Correct Answer - D Given that, A = {1, 2, 3} Now, number of equivalence relations as follows `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_(5)={(1,2,3) hArr A xx A= A^(2)}` ` :. ` Maximum number of equivalence relation on the set A = {1, 2, 3} = 5 |
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