Which is correct relation

The correct relation is Y > ��.

To understand why this relationship is correct, we can look at the definitions and physical natures of Young's modulus (Y) and Poisson's ratio (σ):

1. Young's Modulus (Y):
Young's modulus is defined as the ratio of longitudinal stress to longitudinal strain. It represents the stiffness of a solid material.
Since stress is force per unit area and strain is a dimensionless ratio, Young's modulus has the unit of pressure, which is Newtons per square meter (N/m²) or Pascals (Pa).
For typical solid materials, the value of Young's modulus is extremely large, usually on the order of billions of Pascals (Giga-Pascals, GPa). For example, for steel:

$Y\approx 2\times {10}^{11}{\text{N/m}}^2$

2. Poisson's Ratio (σ):
Poisson's ratio is defined as the ratio of lateral strain to longitudinal strain.
Since it is the ratio of two strain values (which are both dimensionless), Poisson's ratio is a dimensionless number.
Theoretically, the value of Poisson's ratio for any isotropic elastic material must lie within the range:

$-1\le \sigma \le 0.5$

For almost all common solid materials, it has a positive value between 0 and 0.5.

Conclusion:
Since Young's modulus (Y) has an extremely large numerical value, and Poisson's ratio (σ) is a dimensionless value less than 0.5, the numerical value of Y is always much larger than σ.
Therefore, the correct relation is:

$Y>\sigma$