Let be the set of all straight lines in a plane

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let LL be the set of all straight lines in a plane. A relation RR on LL is defined by L1 R L2 if and only if L1 is parallel to L2.L_1 \thinspace R \thinspace L_2 \text{ if and only if } L_1 \text{ is parallel to } L_2. Determine whether RR is reflexive, symmetric and transitive. Hence state whether RR is an equivalence relation, giving a brief reason for each property.

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