Prove that the relation R defined on the set N of natural numbers by xRy `iff 2x^(2) - 3xy + y^(2) = 0` is not symmetric but it is reflexive.

Explanation

To prove that the relation \( R \) defined on the set of natural numbers \( \mathbb{N} \) by \( xRy \) if and only if \( 2x^2 - 3xy + y^2 = 0 \) is not symmetric but is reflexive, we will follow these steps:

### Step 1: Prove that the relation is reflexive

A relation \( R \) is reflexive if for every element \( x \in \mathbb{N} \), it holds that \( xRx \).

1. Let \( x \) be any natural number. We need to check if \( xRx \) holds.

...