Maths-
General
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Question

Let R = {(x, y) : x, y element of A, x + y = 5} where A = {1, 2, 3, 4, 5} then

  1. R is not reflexive, symmetric and not transitive    
  2. R is an equivalence relation    
  3. R is reflexive, symmetric but not transitive    
  4. R is not reflexive, not symmetric but transitive    

The correct answer is: R is not reflexive, symmetric and not transitive


    To define the given statement.
    For the given R= {(x, y) : x, y element of A, x + y = 5}, R can take the values {(1,4),(4,1),(2,3)(3,2)}

    From the values, R is not reflexive since (1,1)/R.


    R is symmetric

    R is not transitive as (1,4)R(4,1)R but (1,1)/R.

    Hence, the given relation is not reflexive, symmetric and not transitive

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