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Set A= {1, 2, 3} R1 and R2 is defined from set A R1= {(1, 1), (1, 2), (2, 2), (2, 3), (3, 3)} R2= {(1, 1), (1, 3), (2, 3)} Is R1 and R2 is transitive. Give reason also

Set A= {1, 2, 3}
R1 and R2 is defined from set A
R1= {(1, 1), (1, 2), (2, 2), (2, 3), (3, 3)}
R2= {(1, 1), (1, 3), (2, 3)}
Is R1 and R2 is transitive. Give reason also

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
8 years ago
A relation on a set is transitive if, when we have (a,b) and (b,c), we have also (a,c).
Hence take R1.. if we take (1,2) and (2,3) .. There is no (1,3). Hence it is non-transitive.
We take R2.. It satisfies the condition. Hence it is transitive.

Thanks & Regards
Bharat Bajaj
askIITians Faculty
IIT Delhi

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