Prove that the relation R defined on set N of natural numbers by x Ry ⟺2x² – 3xy + y² = 0 i.e., by 

2x² – 3x.x + x² = 0; ∀ x ∈ N  

∴ x R x ∀ x ∈ N, Hence R is reflexive.

For x = 1, y = 2 ⇒

2x² - 3xy + y² = 2 × 1² - 3 × 1 × 2 + 2² = 2 – 6 + 4 = 0   ∴1R² for (1, 2) ∈ R

But for (2, 1), x = 2, y = 1   ⇒     2x2 – 3xy + y2 = 2 × 22 – 3 × 2 × 1 + 12 = 8 – 6 + 1 ≠0

∴ (2, 1) ∉ R So, R is not symmetric.