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show that the relation R in the set A={1,2,3}given by R={(1,1)(2,2)(3,3)(1,2)(2,3)} is reflexive but neither symmetric nor transitive

Posted by Yashpal Letv 6 years, 4 months ago

CBSE > Class 12 > Mathematics

1 answers

Divyanshu Mishra 6 years, 4 months ago

For Reflexive : {(1,1),(2,2),(3,3)} € R Hence the relation "R" is Reflexive. For Symmetric : {(1,2),(2,3)} € R but {(2,1),(3,2)} doesn't € R Hence "R" is not symmetric. For transitive : {(1,2)}€R and {(2,3)}€R but {(1,3)} doesn't € "R" Therefore "R" is not transitive Therefore the relation "R" is Reflexive but neither symmetric nor transitive

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