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The relation R={(1,1),(2,2),(3,3)} on th...

The relation `R={(1,1),(2,2),(3,3)}` on the set {1, 2, 3) is

A

symmetric only

B

reflexive only

C

transitive only

D

an equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
D
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Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2),(3,3) , (1,2) ., (2,3)} is reflexive but neither symmetric nor transitive.

Show that the relation R in the set A = {1,2,3,4,5} given by R = {(a,b) : |a-b| is even}, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1,3,5} is related to any element of {2,4}.

Knowledge Check

  • The minimum number of elements that must be added to the relation R={(1,2),(2,3)} on the set {1, 2, 3} so that it is an equivalence relation

    A
    3
    B
    5
    C
    6
    D
    7

  • Inverse relation of {(1,2),(1,3),(2,3)} is

    A
    {(1,2),(1,3),(2,3)}
    B
    {(2,1),(3,1),(3,2)}
    C
    `cancelO`
    D
    {(-1,2,(-1,-3),(-2,-3)}

  • Let R={ (1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A={1,2,3,4} . The relation R is

    A
    a function
    B
    reflexive
    C
    not symmetric
    D
    transitive

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