Maths-
General
Easy

Question

Which one of the following relations on R is equivalence relation

  1. x R subscript 1 end subscript y left right double arrow vertical line x vertical line equals vertical line y vertical line    
  2. x R subscript 2 end subscript y left right double arrow x greater or equal than y    
  3. open x R subscript 3 end subscript y left right double arrow x ∣ y text  (x divides  end text y close parentheses    
  4. x R subscript 4 end subscript y left right double arrow x less than y    

The correct answer is: x R subscript 1 end subscript y left right double arrow vertical line x vertical line equals vertical line y vertical line


    To find the equivalence relation from the given options.
    An equivalence relation is a relation that is reflexive, symmetric and transitive.
    In first option, |x| = |y|
    Reflexive: (x, x) ∈ R
    x = x
    Symmetric: (x, y) ∈ R
    (y, x) ∈ R
    Transitive: (x, y), (y, z) ∈ R
    then (x, z) ∈ R
    x = z
    xR1y ⇔ |x| = |y|

    Hence, option 1 is an equivalence relation.

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