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

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

A

Reflexive but not symmetric

B

Reflexive but not transitive

C

Symmetric and transitive

D

Neither symmetric nor transitive

Text Solution

Verified by Experts

The correct Answer is:
A
As `(1,1),(2,2),(3,3) in R, R ` is reflexive
As `(1,2) in R` but `(2,1) notin R, R` is not symmetric
It can be easily seen that R is transitive
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Knowledge Check

  • 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

  • The relation R={(2,3),(1,1),(1,3),(3,1)} on the set A=(1,2,3) is______

    A
    Reflexive only
    B
    symmetric
    C
    transitive
    D
    Both b and c

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