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NDA 2021 Maths · Mathematics · Sets, Relations and Functions · medium

Every reflexive and symmetric relation on \1,2,3\ is transitive. 2. The identity relation on any non-empty set is an equivalence relation.

Single correct option

Which of the statements is/are correct? 1. Every reflexive and symmetric relation on {1,2,3}\{1,2,3\} is transitive. 2. The identity relation on any non-empty set is an equivalence relation.
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
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Answer: (B) 2 only

Statement 1 fails: {(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}\{(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)\} is reflexive and symmetric but (1,2),(2,3)(1,2),(2,3) are present while (1,3)(1,3) is not. Statement 2 holds since the identity relation is reflexive, symmetric and transitive. Only 2 is correct.
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Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake