all must be done in ML programming language : $(15$ points$)$ Define a function rem$\_$duplicate: $\text{'}\text{'}$a list $->\text{'}\text{'}$a list which takes in input a list and takes out all the duplicates. Test your code with sample input and report result. Examples: rem$\_$duplicate $[]=[]$ rem$\_$duplicate $[1,2,1]=[1,2]$ rem$\_$duplicate $["$a$","$a$","$a$"]=["$a$"]$ rem$\_$duplicate $[[1],[1,2],[1,2,3],[1,2],[4,5]]=[[1],[1,2],[1,2,3],[4,5]]2.(15$ points$)$ Define a function parts: string $*$ string $->$ bool which takes as input, two strings, and returns true if and only if the second string is part of the first string. $($Hint: Use the function explode learned in the class to break strings into lists of characters$)$ Examples: parts$($johnjay$,$ohnj$)=$ true parts$($johnjay$,$jay$)=$ true parts$($johnjay$,$johns$)=$ false