A) 5
B) 3!
C) \[{{2}^{3}}\]
D) \[{{3}^{3}}\]
Correct Answer: A
Solution :
[a] The smallest equivalence relation is the identity relation \[{{R}_{1}}=\{(a,a),(b,b),(c,c)\] Then two ordered pairs of two distinct elements can be added to give three more equivalence relations \[{{R}_{2}}=\{(a,a),(b,b),(c,c),(a,b),(b,a)\}\] Similarly \[{{R}_{3}}\] and \[{{R}_{4}}.\] finally the largest equivalence relation i.e., the universal relation
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