This assignment has to do with converting between sets, bit strings, and shortest latticepaths as we have been studying in class. Sets are represented by lists and are subsets of$[1,2,3,...,$ n$].$ The n$-$bit strings will be lists of length n where each entry is a $0$ or $1($e$.$g$.[1,0,1,1,1,0]$ for a $6-$bit string$).$ Lattice paths of length n will be lists of length n whereeach entry is either the string $$right$$ or the string $$up$($e$.$g$.[$right$,$up$,$right$,$right$,$up$]).$You will write three functions, one from each of the following groups$\mathrm{.}1.$ Sets & Bit Strings$($a$)$ Create a function $$setToBit$$ whose inputs are an integer n and a subset A $[1,2,3,...,$ n$]($so n is the cardinality of the larger set that A is a subset of$).$The function will return an n$-$bit string that corresponds to the subset A$.$ Forinstance, if n $=8$ and A $=[2,3,5,7],$ then your function will return the $8-$bitstring $[0,1,1,0,1,0,1,0]($note that the $1$s are in positions $2,3,5,$ and $7,$ whichcorrespond to the elements of A$).($b$)$ Create a function $$bitToSet$$ whose input is a bit string B$.$ The function willreturn a subset $($i$.$e$.$ list$)$ that corresponds to the bit string B$.$ For instance, ifB $=[1,1,0,0,1,0,0,1],$ then your function will return the subset $[1,2,5,8]\mathrm{.}2.$ Sets & Lattice Paths$($a$)$ Create a function $$setToLattice$$ whose inputs are an integer n and a subsetA $[1,2,3,...,$ n$]($so n is the cardinality of the larger set that A is a subsetof$).$ The function will return a lattice path of length n that corresponds to thesubset A$.$ For instance, if n $=8$ and A $=[2,3,5,7],$ then your function will returnthe $8-$bit string $[$right$,$up$,$up$,$right$,$up$,$right$,$up$,$right$]($note that the $$up$$entries are in positions $2,3,5,$ and $7,$ which correspond to the elements of A$).($b$)$ Create a function $$latticeToSet$$ whose input is a lattice path P $.$ The function willreturn a subset $($i$.$e$.$ list$)$ that corresponds to the lattice path P $.$ For instance, ifP $=[$up$,$up$,$right$,$right$,$up$,$right$,$right$,$up$],$ then your function will returnthe subset $[1,2,5,8]\mathrm{.}3.$ Bit Strings & Lattice Paths$($a$)$ Create a function $$bitToLattice$$ whose input is a bit string B$.$ The functionwill return a lattice path that corresponds to the bit string B$.$ For instance, ifB $=[1,0,1,0,0,1,0,1,1],$ then your function will return the list$[$up$,$right$,$up$,$right$,$right$,$up$,$right$,$up$,$up$].$

$($b$)$ Create a function $$latticeToBit$$ whose input is a lattice path P $.$ The functionwill return a bit string that corresponds to the lattice path P $.$ For instance, ifP $=[$up$,$up$,$right$,$right$,$up$,$right$,$right$,$up$],$ then your function will returnthe bit string $[1,1,0,0,1,0,0,1].$Make sure your functions are well documented. You should have one$-$line comments $($usingthe single line comments with #$)$ written in complete sentences that describe what each lineof code does.