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(B) relation $R$ on a set $L$ is defined as $\alpha R \beta$ if and only if $\alpha \perp \beta$ (line $\alpha$ is perpendicular to line $\beta$).$1$.

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Symmetric

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(B) relation $R$ on a set $L$ is defined as $\alpha R \beta$ if and only if $\alpha \perp \beta$ (line $\alpha$ is perpendicular to line $\beta$).$1$. Reflexivity: For $R$ to be reflexive,$\alpha R \alpha$ must hold for all $\alpha \in L$. This implies $\alpha \perp \alpha$. Since a line cannot be perpendicular to itself,$R$ is not reflexive.$2$. Symmetry: For $R$ to be symmetric,if $\alpha R \beta$,then $\beta R \alpha$ must hold. If $\alpha \perp \beta$,then clearly $\beta \perp \alpha$. Thus,$R$ is symmetric.$3$. Transitivity: For $R$ to be transitive,if $\alpha R \beta$ and $\beta R \gamma$,then $\alpha R \gamma$ must hold. If $\alpha \perp \beta$ and $\beta \perp \gamma$,then $\alpha$ is parallel to $\gamma$ $(\alpha \parallel \gamma)$,not perpendicular. Thus,$R$ is not transitive.Therefore,the relation $R$ is symmetric.

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

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