For a set A, the power set of A is denoted by ${2}^{A}$. If A={5,{6},{7}},which of the following options are TRUE?

 I. $\varnothing \in {2}^{A}$ II. $\varnothing \subseteq {2}^{A}$ III. $\left\{5,\left\{6\right\}\right\}\in {2}^{A}$ IV. $\left\{5,\left\{6\right\}\right\}\subseteq {2}^{A}$

A binary operation $\oplus$ on a set of integers is defined as $x\oplus y={x}^{2}+{y}^{2}$ . Which one of the following statements is TRUE about $\oplus$?