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JEE Main 201322 AprilOnline
Exam
JEE Main
Year
2013
Date
22 April
Mode
Online
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2013 · 22 April · Online · Mathematics · Sets and Relations

Let R=\ (3,3)(5,5),(9,9),(12,12),(5,12),(3,9) , (3,12),(3,5)\ be a...

Let R={(3,3)(5,5),(9,9),(12,12),(5,12),(3,9)R=\{(3,3)(5,5),(9,9),(12,12),(5,12),(3,9), (3,12),(3,5)}(3,12),(3,5)\} be a relation on the set⁡A={3,5,9,12}\operatorname{set} A=\{3,5,9,12\}. Then, RR is :

Options

  1. Areflexive, symmetric but not transitive.
  2. Bsymmetric, transitive but not reflexive.
  3. Can equivalence relation.
  4. Dreflexive, transitive but not symmetric.

Correct answer

D. reflexive, transitive but not symmetric.

Step-by-step solution

Let R={(3,3),(5,5),(9,9),(12,12),(5,12)\mathrm{R}=\{(3,3),(5,5),(9,9),(12,12),(5,12), (3,9),(3,12),(3,5)}(3,9),(3,12),(3,5)\} be a relation on set A={3,5,9,12}\mathrm{A}=\{3,5,9,12\} Clearly, every element of AA is related to itself. Therefore, it is a reflexive. Now, R\mathrm{R} is not symmetry because 3 is related to 5 but 5 is not related to 3 . Also R\mathrm{R} is transitive relation because it satisfies the property that if aRba \mathrm{R} b and bRcb \mathrm{R} c then aRca \mathrm{R} c.
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