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Question

The relation R defined in N as aRb left right double arrow b is divisible by a is

  1. Reflexive but not symmetric    
  2. Symmetric but not transitive    
  3. Symmetric and transitive    
  4. None of these    

The correct answer is: Reflexive but not symmetric


    To define the given relation.
    Given, aRb left right double arrow b is divisible by a
    1R1 = 1 is divisible by 1
    (a, a) ∈ R is Reflexive
    aRb = bRa
    But 2R4 = 4 is divisible by 2 but 4R2 ⇒ 2 is not divisible by 4
    It is not symmetric.

    Hence, the given relations is reflexive but not symmetric.

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