text: 1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
  3. Examples
  
  Transcript
  
  Example 3 Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2) : L1 is perpendicular to L2}. Show that R is symmetric but neither reflexive nor transitive. R = {(L1, L2) : L1 is perpendicular to L2} Check reflexive If R is reflexive, then (L, L) ∈ R Line L cannot be perpendicular to itself So, line L is not perpendicular to line L So, (L, L) ∉ R. ∴ R is not reflexive Check symmetric If L1 is perpendicular to L2 , then L2 is perpendicular to L1 So, if (L1, L2) ∈ R , then (L2, L1) ∈ R. ∴ R is symmetric Check transitive If L1 is perpendicular to L2 & L2 is perpendicular to L3 , then L1 is not perpendicular to L3 , it is parallel to L3 So, if (L1, L2) ∈ R, (L2, L3) ∈ R then , (L1, L3) ∉ R. ∴ R is not transitive
  
  Examples
explanation: The text is a transcript from a mathematics textbook, specifically from Chapter 1 on Relations and Functions. It provides an example that discusses a relation \( R \) defined on the set of all lines in a plane, where \( R = \{(L1, L2) : L1 \text{ is perpendicular to } L2\} \). The example then checks whether the relation \( R \) is reflexive, symmetric, and transitive. The text does not contain a question or an answer to a question; it is a detailed explanation of a mathematical concept.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
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  1. Briefly describe the document and mention if it contains a question or a question and answer.
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distilabel_metadata.role: system
distilabel_metadata.content: 1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
  3. Examples
  
  Transcript
  
  Example 3 Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2) : L1 is perpendicular to L2}. Show that R is symmetric but neither reflexive nor transitive. R = {(L1, L2) : L1 is perpendicular to L2} Check reflexive If R is reflexive, then (L, L) ∈ R Line L cannot be perpendicular to itself So, line L is not perpendicular to line L So, (L, L) ∉ R. ∴ R is not reflexive Check symmetric If L1 is perpendicular to L2 , then L2 is perpendicular to L1 So, if (L1, L2) ∈ R , then (L2, L1) ∈ R. ∴ R is symmetric Check transitive If L1 is perpendicular to L2 & L2 is perpendicular to L3 , then L1 is not perpendicular to L3 , it is parallel to L3 So, if (L1, L2) ∈ R, (L2, L3) ∈ R then , (L1, L3) ∉ R. ∴ R is not transitive
  
  Examples
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text is a transcript from a mathematics textbook, specifically from Chapter 1 on Relations and Functions. It provides an example that discusses a relation \( R \) defined on the set of all lines in a plane, where \( R = \{(L1, L2) : L1 \text{ is perpendicular to } L2\} \). The example then checks whether the relation \( R \) is reflexive, symmetric, and transitive. The text does not contain a question or an answer to a question; it is a detailed explanation of a mathematical concept.
  
  Label: no-question