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Let A = {1, 2, 3}. Then number of equiva...

Let `A = {1, 2, 3}`. Then number of equivalence relations containing (1, 2) is (A) 1 (B) 2 (C) 3 (D) 4

A

1

B

2

C

3

D

4

Text Solution

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B
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Let A = {1, 2, 3} Then show that the number of relations containing (1, 2) and (2, 3) which are reflexive and transitive but not symmetric is three.

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Knowledge Check

  • Let A = {1,2,3}. Then number of relations containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is

    A
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    B
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  • The maximum number of equivalence relations on the set A = {1,2,3} are ..........

    A
    1
    B
    2
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    3
    D
    7

  • If A = {1,2,3} and consider the relation R = {(1,1), (2,2) , (3,3) , (1,2) ,(2,3), (1,3)} . Then R is .......

    A
    reflexive but not symmetric
    B
    reflexive but not transitive
    C
    symmetric and transitive
    D
    neither symmetric, nor transitive

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