Example 2 - Let R = {(T1, T2) : T1 is congruent to T2} - Examples

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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
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Example 2, Let T be the set of all triangles in a plane with R a relation in T given by R = {(T1, T2) : T1 is congruent to T2}. Show that R is an equivalence relation. R = {(T1, T2) : T1 is congruent to T2}. Check reflexive Since every triangle is congruent to itself Triangle T is congruent to triangle T ∴ (T , T) ∈ R So, R is reflexive, Check symmetric If T1 is congruent to T2 , then T2 is congruent to T1 So, if (T1, T2) ∈ R , then (T2, T1) ∈ R. Hence , R is symmetric. Check transitive If T1 is congruent to T2 , & T2 is congruent to T3 then T1 is congruent to T3 So, if (T1, T2), (T2, T3) ∈ R , then (T1, T3) ∈ R. So, R is transitive Since R is reflexive, symmetric & transitive. Therefore, R is an equivalence relation.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.