Mark the correct alternative in the following question: The relation S defined on the set R of all real number by the rule aSb if a $\geq$ b is _______________ .

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KollegeApply · Accepted Answer

We have, S = {(a, b) : a $\geq$ b; a, b ∈ R} As, a=a ∀ a ∈ R $\Rightarrow$ (a, a) ∈ S So, S is reflexive relation Let (a, b) ∈ S $\Rightarrow$ a $\geq$ b But b $\leq$ a $\Rightarrow$ (b, a) ∉ S So, S is not symmetric relation Let (a, b) ∈ S and (b, c) ∈ S $\Rightarrow$ a $\geq$ b and b $\geq$ c $\Rightarrow$ a $\geq$ c $\Rightarrow$ (a, c) ∈ S So, S is transitive relation Hence, The relation S defined on the set R of all real number by the rule aSb if a $\geq$ b is reflexive, transitive but not symmetric.

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