Question Details
| Board | CBSE |
| Book | NCERT Textbook |
| Class | 12 |
| Subject | Mathematics |
| Chapter | 1 [Relations and Functions] |
| Exercise | 1.1 |
| Question No. | 6 |
| Question Type | Exercise |
Show that the relation \(R\) in the set \(\{1,2,3\}\) given by \(R=\{(1,2),(2,1)\}\) is symmetric but neither reflexive nor transitive.
Expert Answer
Solution:
\[
A=\{1,2,3,\}: R=\{(1,2),(2,1)\}
\]
(a) Reflexive : \(R=\{(a, a)\}\) where \(a \in A\). \(=\{(1,1),(2,2),(3,3)\}\) this is not true so not reflexive.
(b) Symmetric : \(R=\left\{\left(a_1, a_2\right)\right\}\) and \(R=\left\{\left(a_2, a_1\right)\right\}\) as \((1,2) \in R\) as well as \((2,1) \in R\). So symmetric.
(c) Transitive : \(R=\left\{\left(a_1, a_2\right)\right\}\) and \(R=\left\{\left(a_2, a_3\right)\right\}\). Not transitive.
Verified Answer
5/5
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