First slide

Relations XII

Question

$The relation R defined on the set N of natural numbers by x R y \Leftrightarrow 2 x^{2} - 3 x y + y^{2} = 0 is$

Easy

A

symmetric but not reflexive
B

only symmetric
C

not symmetric but reflexive
D

equivalence

Solution

$\begin{array}{l} (i) xRx \Leftrightarrow 2 x^{2} - 3 x \cdot x + x^{2} = 0; \forall x \in N \\ So, R is reflexive \end{array}$
$\begin{array}{l} (ii) For x = 1, y = 2; 2 x^{2} - 3 xy + y^{2} = 0 \\ ∴ 1 R 2 but 2 \times 1^{2} - 3 \times 2 \times 1 + 2^{2} = 3 \neq 0 \end{array}$
So, 2 is not R- related to 1.
So, R is not symmetric.

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