Let x be a real number between 0 and 1. Which of the following statements is/are correct?
I. x² > x³.
II. x > x.
Select the correct answer using the code given below:

The correct answer is I only.

Let us analyze the given statements step-by-step for any real number $x$ such that $0<x<1$.

Analyzing Statement I: $x^2>x^3$

Since $x$ is a positive real number between 0 and 1, multiplying both sides of the inequality $x<1$ by $x^2$ (which is positive) maintains the inequality sign:

$x^2·x<x^2·1$

$x^3<x^2$

This is equivalent to $x^2>x^3$.

For example, if $x=0.5$:

$x^2={0.5}^2=0.25$

$x^3={0.5}^3=0.125$

Since $0.25>0.125$, Statement I is correct.

Analyzing Statement II: $x>x$

For any real number, a quantity cannot be strictly greater than itself. Thus, $x>x$ is false for all values of $x$.

Therefore, only statement I is correct.