Parallelism is Reflexive Relation

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Let $S$ be the set of straight lines in the plane.

For $l_1, l_2 \in S$, let $l_1 \parallel l_2$ denote that $l_1$ is parallel to $l_2$.

Then $\parallel$ is a reflexive relation on $S$.


By definition of parallel lines, the contemporary definition is for a straight line to be declared parallel to itself.

Hence for a straight line $l$:

$l \parallel l$

Thus $\parallel$ is seen to be reflexive.


Also see