JEE MainMathematicsModerateRelation

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

Show answer and solution

(i)

xRx \Leftrightarrow 2x^{2} - 3x \cdot x + x^{2} = 0\forall x \in \mathbb{N}

R is reflexive.
(ii) for x=1, y=2

2x^{2} - 3xy + y^{2} = 2 \times 1 - 3 \times 1 \times 2 + 4 = 2 - 6 + 4 = 0

But for y=1, x=2

2x^{2} - 3xy + y^{2} = 2x(2)^{2} - 3 \times 1 \times 2 + (1)^{2} = 8 - 6 + 1 = 3 \neq 0

So 1 R 2 but 2 not R 1
So R is not symmetric.

Source: Grass-G / M-17 Mathematics Paper 26 Nov Second.docx

Need a video for this idea?

Scan any doubt from your notes and get a whiteboard explanation.