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BITSAT2024MathematicsSets and RelationsActual

Let R be the relation "is congruent to" on the set of all triangles in a plane is

Options

  1. AReflexive only
  2. BSymmetric only
  3. CSymmetric and reflexive only
  4. DEquivalence relation

Correct answer

D. Equivalence relation

Step-by-step solution

Let S denote the set of all triangles in a plane. Let R be the relation on S defined by ( ₁, ₂ ) triangle ₁ ₂ : (i) Let any triangle S , we have ₁ ₂ ( , ) R S R is reflexive on (ii) Let ₁, ₂ ~S , such that ( ₁, ₂ ) R , then ₁ ₂ ₂ ₁ ( ₂, ₁ ) R R is symmÄ™tric (iii) Again, let ₁, ₂, ₃ ~S such that ( ₁, ₂ ) R and ( ₂, ₃ ) R ₁ ₂ ₃ ( ₁, ₂ ) R R is transitive. R is an equivalence relation.

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