On the set of lines in a plane, L₁ R L₂ if L₁ is perpendicular to L₂. Which of these describes R?

Question 32

MediumOriginal question

On the set of lines in a plane, $L_1 \mathrel{R} L_2$ if $L_1$ is perpendicular to $L_2$ . Which of these describes $R$ ?

Symmetric and transitive, but not reflexiveCorrect answerYour answerSymmetric onlyCorrect answerYour answerReflexive and symmetric, but not transitiveCorrect answerYour answerNeither reflexive, symmetric nor transitiveCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

No line is perpendicular to itself: not reflexive. If $L_1 \perp L_2$ , then $L_2 \perp L_1$ : symmetric.
If $L_1 \perp L_2$ and $L_2 \perp L_3$ , then $L_1$ is parallel to $L_3$ , not perpendicular: not transitive.

Worth noting

Two right-angle turns bring a line back parallel to where it started.

Concept: Testing a relation given by a rule
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsTypes of relations

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Ten questions from Relations & Functions, at your own pace.

On the set of lines in a plane, L1RL2L_1 \mathrel{R} L_2L1​RL2​ if L1L_1L1​ is perpendicular to L2L_2L2​. Which of these describes RRR?

Explanation

On the set of lines in a plane, $L_1 \mathrel{R} L_2$ if $L_1$ is perpendicular to $L_2$ . Which of these describes $R$ ?