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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

Let R = \ (1, 3), (4, 2), (2, 4), (2, 3), (3,1)\ be a relation on...

Let R={(1,3),(4,2),(2,4),(2,3),(3,1)}R = \left\{\left(1, 3\right), \left(4, 2\right), \left(2, 4\right), \left(2, 3\right), (3,1)\right\} be a relation on the set A={1,2,3,4}A = \left\{1,2, 3,4\right\}. The relation RR is

Options

  1. AReflexive
  2. BTransitive
  3. CNot symmetric
  4. DA function

Correct answer

C. Not symmetric

Step-by-step solution

Clearly, (1,1),(2,2),(3,3),(4,4)(1,1) , (2,2) , (3,3) , (4,4) are not in R.<br/><br/>So,itisnotreflexive<br/><br/>Weobservethat(2,3)R.<br /><br />So, it is not reflexive<br /><br />We observe that \left(2,3\right)\in Rbut\left(3, 2\right)\notin R,soitisnotsymmetric.<br/><br/>Clearly,(1,3)so it is not symmetric.<br /><br />Clearly, \left(1,3\right)\in Rand\left(3,1\right)∈\in\mathbb{R},but(1,1), but\left(1,1\right)\notin R.

So, it is not transitive.

Since, \left(2,4\right)and(2,3)and \left(2,3\right) are in RR. So, it is not a function.
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