$2$ESn,m S $-$ nmESUse structural induction to prove that all members of S are powers of $2($with the exponent being a positive inte your response, write "power of $2"$ instead of "power of $2$ with positive integer exponent" for brevity. Your proof concise.Compose your answer in the textbox. Do not copy and paste the complete problem text or these instruction: textbox. You may copy and paste unicode math symbols from the problem text for use in your answer.DO NOT USE THE CANVAS EQUATION EDITOR.For your convenience, here are some additional unicode superscripts for you to copy and paste. Not all of th symbols will be needed: $\backslash$deg $123456789+-=($abc def ghtikimn@prstuvwxy.Remember to avoid the following common mistakes on structural induction proofs: trying to force structural induction into linear induction. The inductive step is not about going from $"$n$"$ to tracing a logical chain reaction through a tree structure, not a line. treating the first generation descendants as part of the base case. re$-$explaining the logic of structural induction inside the inductive step. justifying the inductive hypothesis with the base case. assuming that the recursion rules defining the recursively defined sets are always applied in some spec or in combination with each other. Confusing the definition of the set S with what you are proving about S$.$ Confusing what you already know with what you want to verify in the base case.