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BITSAT2017MathematicsSets and RelationsActual

Let A = 1 , 2 , 3 , 4 , 5 and R be a relation defined by R = ( x , y ) : x , y ∈ A , x + y = 5 . Then, R is

Options

  1. Areflexive and symmetric but not transitive
  2. Ban equivalence relation
  3. Cneither reflexive nor transitive
  4. Dneither reflexive nor symmetric but transitive

Correct answer

C. neither reflexive nor transitive

Step-by-step solution

We first write the elements of the set R . i.e. R = ( 1 , 4 ) , ( 4 , 1 ) , ( 2 , 3 ) , ( 3 , 2 ) Since, ( 1 , 1 ) ∉ R ⇒ R is not reflexive. Now as, ( 1 , 4 ) ∈ R ⇒ ( 4 , 1 ) ∈ R and ( 2 , 3 ) ∈ R ⇒   ( 3 , 2 ) ∈ R So, R is symmetric Now, ( 1 , 4 ) ∈ R and ( 4 , 1 ) ∈ R Thus, R is not transitive. Hence, R is symmetric but neither reflexive nor transitive.

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