# The relation S defined on the set R of all real number by the rule a Sb iff a ≥ b isA. an equivalence relationB. reflexive, transitive but not symmetricC. symmetric, transitive but not reflexiveD. neither transitive nor reflexive but symmetric

S: a S b a ≥ b

Since a=a a R, therefore a ≥ a always. Hence (a, a) always belongs to S a R. Therefore, S is reflexive.

If a ≥ b then b ≤ a b ≥ a. Hence if (a, b) belongs to S, then (b, a) does not always belongs to S. Hence S is not symmetric.

If a ≥ b and b ≥ c, therefore a ≥ c. Hence if (a, b) and (b, c) belongs to S, then (a, c) will belong to S a, b, cR. Hence, S is transitive.

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