First slide

Relations XII

Question

$Let R be a relation from ℝ (set of real numbers) to ℝ defined by R = {(a, b) ∣ a, b \in ℝ and$ $a - b + \sqrt{3} is an irrational number} . The relation R is$

Moderate

A

an equivalence relation
B

transitive only
C

reflexive only
D

symmetric only

Solution

$R = {(a, b) ∣ a, b \in R and a - b + \sqrt{3} is an irrational number}, then R is reflexive$
$(\sin c e a R a = a - a + \sqrt{3} = \sqrt{3} which is an irrational number) \sqrt{3} R 1 = \sqrt{3} - 1 + \sqrt{3} = 2 \sqrt{3} - 1 which$
$is an irrational number but 1 R \sqrt{3} = 1 - \sqrt{3} + \sqrt{3} = 1 which is not irrational number$
$∴ R is not symmetric$
$Also R is not transitive \begin{array}{l} (∵ \sqrt{3} R 1 and 1 R 2 \sqrt{3} but \sqrt{3} R 2 \sqrt{3} \\ \Rightarrow \sqrt{3} - 2 \sqrt{3} + \sqrt{3} = 0) \\ Hence, R is not an equivalence relation \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App