If $x, y \in \mathbb{R}$ then match List-I with List-II

List-I	List-II
(A) $\vert x\vert < \vert y\vert$	(I) iff $x^2 > y^2$
(B) $\vert x\vert > \vert y\vert$	(II) iff $x^2 \le y^2$
(C) $\vert x\vert \le \vert y\vert$	(III) iff $x^2 < y^2$
(D) $\vert x\vert \ge \vert y\vert$	(IV) iff $x^2 \ge y^2$

Choose the correct answer from the options given below:

For any real number $a$, $|a|^2 = a^2$.

Since absolute values are always non-negative, both sides of any inequality involving $|x|$ and $|y|$ can be safely squared without flipping the inequality sign.

---

(A) $|x| < |y|$

$|x|^2 < |y|^2$

$x^2 < y^2$

$(A) \rightarrow (III)$

---

(B) $|x| > |y|$

$|x|^2 > |y|^2$

$x^2 > y^2$

$(B) \rightarrow (I)$

---

(C) $|x| \leq |y|$

$|x|^2 \leq |y|^2$

$x^2 \leq y^2$

$(C) \rightarrow (II)$

---

(D) $|x| \geq |y|$

$|x|^2 \geq |y|^2$

$x^2 \geq y^2$

$(D) \rightarrow (IV)$

---

$(A) \rightarrow (III)$, $(B) \rightarrow (I)$, $(C) \rightarrow (II)$, $(D) \rightarrow (IV)$