$8.)$ Please solve the following problem $($parts a$-$f$).$ Show all work and give detailed explanation.

a$.$ i$)$Given S $=\{$ z$,$ b$,$ g $\}$

List all subsets of S$.$

a$.$ ii$)$ Given S$=\{$ z$,$ b$,$ g$,$ r $\}$

List all subset of S

b$.)$ List all substrings of cdef

c$.)$ Given S$=100,$ How many subsets can be created?

d$.)$ Create a pseudocode for the following function decode$($x$)$

Input: Int x$,$ set S of size n$,$ where $<(21)$

Output: the dubset represented by the binary digit

Example$1$ Input: decode$(7)$ S$=$A$,$B$,$C

Because binary$(7)=111$ that means we include all members of

set S

Output:$\{$A$,$B$,$C$\}$

Example$2$ Input: decode$(5)$ S$=$A$,$B$,$C

Because binary$(5)=101$ that means we include first and last

member

Output:$\{$A$,$C$\}$

e$.)$ Provide pseudocode the creates list all subsets of any

set S$?$

f$.)$ Provide pseudocode for all possible substrings of a

single string your code could list duplicates.