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JEE Main 201816 AprilOnline
Exam
JEE Main
Year
2018
Date
16 April
Mode
Online
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2018 · 16 April · Online · Mathematics · Sets and Relations

Let N denote the set of all natural numbers. Define two binary...

Let NN denote the set of all natural numbers. Define two binary relations on NN as R1={(x,y)∈N×N:2x+y=10}{R}_{1} = \left\{\left(x, y\right) \in N \times N: 2x + y = 10\right\} and R2={(x,y)∈N×N:x+2y=10}{R}_{2} = \left\{\left(x, y\right) \in N \times N: x + 2y = 10\right\}. Then

Options

  1. Aboth R1{R}_{1} and R2{R}_{2} are transitive relations
  2. Brange of R2{R}_{2} is \left\{1, 2, 3, 4\right\}
  3. Crange of R1{R}_{1} is \left\{2, 4, 8\right\}
  4. Dboth R1{R}_{1} and R2{R}_{2} are symmetric relations

Correct answer

B. range of R2{R}_{2} is \left\{1, 2, 3, 4\right\}

Step-by-step solution

R1={R}_{1} =\left\{\left(1, 8\right), \left(2, 6\right), \left(3, 4\right), \left(4, 2\right)\right\}

R2={(8,1),(6,2),(4,3),(2,4)}{R}_{2} = \left\{\left(8, 1\right), \left(6, 2\right), \left(4, 3\right), \left(2, 4\right)\right\} }

Range of R2={1,2,3,4}{R}_{2} = \left\{1, 2, 3, 4\right\}
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