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NCERT Class 12 · Ch 1 Exercise 1.1 · Q13

NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 13

On all polygons, P₁RP₂ iff they have the same number of sides. Prove equivalence and describe the class of a right triangle with sides 3,4,5.

💡 Concept Hints

  1. The relation uses the number of sides, not similarity.
  2. Work through the definitions using the stated domain and codomain; justify a failed universal property with one valid counterexample.

✅ Step-by-Step Solution

Final Answer: Its class is the set of all triangles.
  1. Let s(P) be the number of sides. Equality s(P₁)=s(P₂) is reflexive and symmetric.
  2. Equality is also transitive, so the relation is an equivalence relation.
  3. The given polygon has three sides. Its class therefore contains every polygon with three sides, namely all triangles, with no restriction on side lengths or angles.

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