First slide

Relations XII

Question

Let R be a relation defined on the set of real numbers by $a R b \Leftrightarrow 1 + a b > 0$ . Then R is

Moderate

A

reflexive, symmetric, but not transitive
B

symmetric, transitive, but not reflexive
C

symmetric, not reflexive, not transitive
D

reflexive, anti symmetric, not transitive

Solution

$\begin{array}{l} 1 + a^{2} > 0 \forall a \in R \Rightarrow (a, a) \in R \Rightarrow R is reflexive \\ i f 1 + ab > 0 t h e n 1 + b a > 0 \Rightarrow R i s symmetric \\ here (- 2, 0) \in R \underset{}{\underline{and}} (0, 3) \in R \\ but (- 2, 3) \notin R \\ ∴ R is not transitive \end{array}$

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