Let $A_{1}, A_{2}, A_{3}$ be regions in the $x y$-plane defined by $$ \begin{array}{l} A_{1}=\left\{(x, y): x^{2}+2 y^{2} \leq 1\right\} \\ A_{2}=\left\{(x, y):|x|^{3}+2 \sqrt{2}|y|^{3} \leq 1\right\} \end{array} $$ $A_{3}=\{(x, y): \max (|x|, \sqrt{2}|y|) \leq 1$. Then

• A

  $\mathrm{A}_{1} \supset \mathrm{A}_{2} \supset \mathrm{A}_{3}$
• B

  $A_{3} \supset A_{1} \supset A_{2}$
• C

  $\mathrm{A}_{2} \supset \mathrm{A}_{3} \supset \mathrm{A}_{2}$
• Correct answer
  D

  $A_{3} \supset A_{2} \supset A_{1}$

Hence, the correct answer is option: 'D'.