Question

write largest equivalence relation on the set A, where A= {1,2,3}​

Answer 1

Answer:

Given, set A = {1, 2, 3} Now, the number of equivalence relations as follows R1 = {(1, 1), (2, 2), (3, 3)} R2 = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)} R3 = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)} R4 = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)} R5 = {(1, 2, 3) ⇔ A x A = A2} Thus, maximum number of equivalence relation is ‘5’.

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