The relation `S` defined on the set `R` of all real number by the rule `a\ S b` iff `ageqb` is (a) equivalence relation (b)reflexive, transitive but not symmetric (c)symmetric, transitive but not reflexive (d) neither transitive nor reflexive but symmetric

Answer

b) reflexive,transitive but not symmetric

Explanation

Since `a=a forall a in R`,

therefore `a geq a `always.

Hence `(a, a)` always `belongs to S forall a in R`.

Therefore, {S} is reflexive.



If `a geq b ` then `b leq a neq b geq a`.

Hence if `(a, b) belongs to S`, then `(b, a) `does not always `belongs to S`.

Hence S is not symmetric.


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