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JEE Main2018MathematicsSets and RelationsActual

Let N denote the set of all natural numbers. Define two binary relations on N as R 1 = x , y ∈ N × N : 2 x + y = 10 and R 2 = x , y ∈ N × N : x + 2 y = 10 . Then

Options

  1. Aboth R 1 and R 2 are transitive relations
  2. Brange of R 2 is 1 , 2 , 3 , 4
  3. Crange of R 1 is 2 , 4 , 8
  4. Dboth R 1 and R 2 are symmetric relations

Correct answer

B. range of R 2 is 1 , 2 , 3 , 4

Step-by-step solution

R 1 = 1 , 8 ,   2 , 6 ,   3 , 4 ,   4 , 2 R 2 = 8 , 1 ,   6 , 2 ,   4 , 3 ,   2 , 4 Range of R 2 = 1 , 2 , 3 , 4

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