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Question

Let R={(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)} be a relation on the set A={3,6,9,12}. Then the relation is

A
Reflexive and transitive only
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B
Reflexive only
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C
Reflexive, symmetric and transitive
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D
Reflexive but neither symmetric nor transitive
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Solution

The correct option is A Reflexive and transitive only
(i) It is reflexive relation as all ordered pairs (3,3),(6,6),(9,9),(12,12) are present in R
(ii)R is not symmetric as (6,12)R but (12,6)R
(iii) For transitive if (a,b),(b,c)R(a,c)R

As the given relation R satisfies the above condition.
Hence R is transitive.

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