A) An equivalence relation on R
B) Reflexive, transitive but not symmetric
C) Symmetric, Transitive but not reflexive
D) Neither transitive not reflexive but symmetric
Correct Answer: B
Solution :
For any\[a\in R\], we have \[a\ge a,\]Therefore the relation R is reflexive but it is not symmetric as (2, 1) \[\in R\] but (1, 2) \[\notin R\]. The relation R is transitive also, because \[(a,b)\in R,(b,c)\in R\] imply that \[a\ge b\]and \[b\ge c\]which is turn imply that\[a\ge c\].
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