Case Study: Decoding Relations

Topic: Relations and Functions (Class 12 Mathematics)

The Problem

A classroom teacher is assessing her students on the concept of “Relations.” She defines Set A = {1, 2, 3} and writes five relations on this set:

  • R₁ = {(2, 3), (3, 2)}
  • R₂ = {(1, 2), (1, 3), (3, 2)}
  • R₃ = {(1, 2), (2, 1), (1, 1)}
  • R₄ = {(1, 1), (1, 2), (3, 3), (2, 2)}
  • R₅ = {(1, 1), (1, 2), (3, 3), (2, 2), (2, 1), (2, 3), (3, 2)}

Questions

  1. Identify the relation, which is reflexive, transitive but not symmetric.
  2. Identify the relation which is reflexive and symmetric but not transitive.
  3. (a) Identify the relations which are symmetric but neither reflexive nor transitive.
    OR
    (b) What pairs should be added to R₃ to make it an equivalence relation?
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