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NCERT Class 12 · Ch 1 Exercise 1.1 · Q7

NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 7

On the books in a college library, xRy iff x and y have the same number of pages. Prove that R is an equivalence relation.

💡 Concept Hints

  1. Express the relation as equality of a numerical attribute.
  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: R is an equivalence relation.
  1. Let p(x) be the page count of book x. Then xRy means p(x)=p(y).
  2. p(x)=p(x), so R is reflexive. Equality is symmetric, so xRy⇒yRx.
  3. If p(x)=p(y) and p(y)=p(z), then p(x)=p(z); thus R is transitive. All three properties hold.

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