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Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) : T1 is congruent to T2}. Show that R is an equivalence relation.

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Answered by Anonymous

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Solution: R is reflexive, since every triangle is congruent to itself. Further,(T1, T2) ∈ R ⇒ T1is congruent to T2 ⇒ T2is congruent to T1 ⇒ (T2, T1) ∈ R. Hence,R is symmetric. Moreover, (T1, T2), (T2, T3) ∈ R ⇒ T1 is congruent to T2 and T2 iscongruent to T3 ⇒ T1 is congruent to T3 ⇒ (T1,T3) ∈ R. Therefore, R is an equivalence relation.

Answered by LUUL

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Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) : T1 is congruent to T2}. Show that R is an equivalence relation.​

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Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) : T1 is congruent to T2}. Show that R is an equivalence relation.