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The relation R is defined in the set 1 , 2 , 3 , 4 , 5 , 6 as R = ( a , b ) : b = a + 1 , then

Options

  1. AR is neither reflexive nor symmetric nor transitive
  2. BR is neither reflexive nor symmetric but transitive
  3. CR is not reflexive but symmetric and transitive
  4. DR is reflexive, symmetric and transitive

Correct answer

A. R is neither reflexive nor symmetric nor transitive

Step-by-step solution

Let, A = 1 , 2 , 3 , 4 , 5 , 6 The relation R is defined on set A is R = a , b : b = a + 1 . Therefore, R = ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) , ( 4 , 5 ) , ( 5 , 6 ) Now, 6 ∈ A but ( 6 , 6 ) ∉ R . Therefore, R is not reflexive. It can be observed that ( 1 , 2 ) ∈ R but ( 2 , 1 ) ∉ R . Therefore, R is not symmetric. Now, ( 1 , 2 ) , ( 2 , 3 ) ∈ R but ( 1 , 3 ) ∉ R . Therefore, R is not transitive. Hence, R is neither reflexive nor symmetric nor transitive

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