Let us define a relation R for real numbers as aRb if a ≥ b. Then R is
A
an equivalence relation
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B
reflexive, transitive but not symmetric
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C
symmetric, transitive but not reflexive
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D
neither transitive nor reflexive but symmetric.
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Solution
The correct option is B reflexive, transitive but not symmetric a≥a, for all 'a' real,∴R is reflexive.a≥b that does not necessarily mean b≥a.∴R is not symmetric.If (a,b) and (b,c)∈R⇒a≥b and b≥c⇒a≥c⇒(a,c)∈R∴R is transitive.