Question
Let be the set of all lines in a plane and be the relation in defined as . Show that is symmetric but neither reflexive nor transitive.
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Text solutionVerified
Given the relation is defined as .
Now this relation is not reflexive as does not hold as every line is not perpendicular to itself.
The relation is symmetric as gives . [ As if is perpendicular to then is also perpendicular to ].
The relation is not transitive as does not gives . [ As, if is perpendicular to and is perpendicular to then may of may not be perpendicular to ]
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Question Text | Let be the set of all lines in a plane and be the relation in defined as . Show that is symmetric but neither reflexive nor transitive. |
Answer Type | Text solution:1 |
Upvotes | 150 |