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  • Check if the relation R in the set of real numbers defined as R = {(a, b) : a < b} is (i) symmetric, (ii) transitive  

Check if the relation R in the set of real numbers defined as R = {(a, b) : a < b} is (i) symmetric, (ii) transitive

 

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Given: R = {(a, b) : a < b} 

\\ $ (i) 1,2 $ \in $ R as $ 1<2 \Rightarrow(1,2) \in R \\ 2 \nless 1 \Rightarrow(2,1) \notin R \\ $ Hence R is not symmetric $ \\\\\ $ (ii) $ \operatorname{Let}(a, b) \in R$ and $(b, c) \in R \\ \Rightarrow a<b$ and $b<c$ $ \\ \Rightarrow a<c \\ \Rightarrow(a, c) \in R \\ $Hence R is transitive.

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Safeer PP

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