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NDA 1 2024 Maths, question 23

Topic: Algebra

Q23

Let RR be a relation on the open interval (−1,1)(-1,1) and is given by R=R= {(x,y):∣x+y∣<2(x,y):|x+y|<2}. Then which one of the following is correct ?

  1. (a) RR is reflexive but neither symmetric nor transitive
  2. (b) RR is reflexive and symmetric but not transitive
  3. (c) RR is reflexive and transitive but not symmetric
  4. (d) RR is an equivalence relationCorrect answer

Solution.

Answer: (d) RR is an equivalence relation

  1. For any x,y in (−1,1), |x+y|≤|x|+|y|<2.
  2. Hence R is the entire Cartesian product A×A.
  3. This universal relation is reflexive, symmetric and transitive, so it is an equivalence relation.