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  4. Let L denote the set of all straight lines in a plane. Let a relation R be defined by α R β Leftrightarrow α perp β, α, β ∈ L. Then R is

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

NTA AbhyasNTA Abhyas 2022

Solution:

Here $\alpha R \beta \Leftrightarrow \alpha \perp \beta$
$\therefore \alpha \perp \beta \Leftrightarrow \beta \perp \alpha$
Hence, R is symmetric.
But, $\alpha \perp \alpha$ and if $\alpha \perp \beta \,\&\, \beta \perp \gamma$
$ \Rightarrow \alpha \perp \gamma$