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To prove relation reflexive, transitive, symmetric and equivalent
Example 4 Important
Ex 1.1, 6
Ex 1.1, 15 (MCQ) Important
Ex 1.1, 7
Ex 1.1, 1 (i)
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Ex 1.1, 5 Important
Ex 1.1, 10 (i)
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Example 5
Example 6 Important
Example 2
Ex 1.1, 12 Important
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Example 3 You are here
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Misc 3 Important
Example 19 Important
Example 18
To prove relation reflexive, transitive, symmetric and equivalent
Last updated at June 6, 2023 by Teachoo
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