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(B) relation $R$ is defined on the set $L$ of all straight lines in a plane as $\alpha R\beta \Leftrightarrow \alpha \perp \beta$.$1$. Reflexive: For

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Symmetric

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(B) relation $R$ is defined on the set $L$ of all straight lines in a plane as $\alpha R\beta \Leftrightarrow \alpha \perp \beta$.$1$. Reflexive: For $R$ to be reflexive,$\alpha R\alpha$ must hold for all $\alpha \in L$. This implies $\alpha \perp \alpha$,which is false because a line cannot be perpendicular to itself. Thus,$R$ is not reflexive.$2$. Symmetric: For $R$ to be symmetric,$\alpha R\beta$ must imply $\beta R\alpha$. If $\alpha \perp \beta$,then clearly $\beta \perp \alpha$. Thus,$R$ is symmetric.$3$. Transitive: For $R$ to be transitive,$\alpha R\beta$ and $\beta R\gamma$ must imply $\alpha R\gamma$. If $\alpha \perp \beta$ and $\beta \perp \gamma$,then $\alpha$ and $\gamma$ are both perpendicular to $\beta$,which means $\alpha \parallel \gamma$. Therefore,$\alpha R\gamma$ is false. Thus,$R$ is not transitive.Conclusion: $R$ is symmetric.

Let $L$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R\beta \Leftrightarrow \alpha \perp \beta$,where $\alpha, \beta \in L$. Then $R$ is

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