Example 3 - Let R = {(L1, L2) : L1 is perpendicular to L2} - To prove relation reflexive, transitive, symmetric and equivalent

Example 3 - Chapter 1 Class 12 Relation and Functions - Part 2

  1. Chapter 1 Class 12 Relation and Functions (Term 1)
  2. Serial order wise
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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

Example 1

Example 2

Example 3 You are here

Example 4 Important

Example 5

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Example 7

Example 8

Example 9

Example 10

Example 11 Important

Example 12 Important

Example 13 Important

Example 14 Important

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.