Question Details
| Board | CBSE |
| Book | NCERT Textbook |
| Class | 12 |
| Subject | Mathematics |
| Chapter | 1 [Relations and Functions] |
| Exercise | 1.1 |
| Question No. | 4 |
| Question Type | Exercise |
Show that the relation R in R defined as R=\{(a, b): a \leq b\}, is reflexive and transitive but not symmetric.
Expert Answer
A=(-\infty, \infty) or R
R=\{(a, b): a \leq b\}
(a) Reflexive : R=\{(a, a): a \leq a\} so reflexive.
(b) Symmetric : R=\left\{\left(a_1, a_2\right): a_1 \leq a_2\right\}
R=\left(a_2, a_1\right): a_2 \leq a_1 so not symmetric.
(c) Transitive : R=\left\{\left(a_1, a_2\right): a_1 \leq a_2\right\} and
R=\left\{\left(a_2, a_3\right): a_2 \leq a_3\right\}
Thus, a_1 \leq a_2 \leq a_3
\Rightarrow a_1 \leq a_3 so transitive.
. Verified Answer
5/5
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