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
The content structure is a transcript of a mathematical example from a textbook, discussing the properties of a relation defined on the set of all lines in a plane.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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
user
The content structure is a transcript of a mathematical example from a textbook, discussing the properties of a relation defined on the set of all lines in a plane.

TYPE: NO_QUESTION