Match the following recursively defined sets to its descriptions Basis step: $0$ S$.$ Recursive$[$ Choose step: if x E S then x$+2$ES Basis step: $1$ E S$.$ Recursive step: if x E S then x$+2$ E S and X$-2$ E S Basis step: $1$ E S and $2$ S$.[$ Recursive step: if x S then x$+3$ Choose$]$ E S Basis step: $1$ E S$.$ Recursive step: if X E S then $2$x E S I Choose $]$ Choose$]$ The set of odd integers. The set of two powers. That is $(2$nln is a non$-$negative integerj S is the set of non$-$negative even integers. The set of positive integers that are not divisible by $3.$Let S be a set of strings defined recursively as follows Basis Step: $0$ ES Recursive Step: if a $$ s$,$ then $2$a$0$ s and $2$aa$1$e S$.$ Note: If a and b are strings then ab is the concatenation of a and b$.$ For instance, if a $0211$ and b $201$ then ab $0211201.)$ Check all the elements of the set S that are produced by the first $2$ applications of the recursive definition. Hint: The set So contains all the elements that are defined in the basis step. The set Si contains all the elements that are obtained by applying the recursive definition to each element of the set So The set S contains all the elements that are obtained by applying the recursive definition to each element of the set Si The elements of S that are produced by the first two applications of the recursive definitions are the elements of the set S oU S$,$ U S$0200200122000220010220020012200120011220012200112012200002200020001222001012200100$