The powerset of a set S is defined as the set of all subsets of S (including the empty set). For example, the powerset of {1,2} is {{1,2}, {1}, {2}, {}}. Write an SML function called powerset: 'a lista list list that when given a list representation of a set as input returns its powerset as output.
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- Write a function split n l that splits the list l and returns a pairof lists containing the first n elements of l and the rest of l, wheresplit has the type int -> ’a list -> (’a list * ’a list). For ex-ample, split 3 [1,2,3,4,5] returns the pair ([1,2,3], [4,5]) andsplit 3 [1,2,3] returns ([1,2,3], []).Write a function that takes a list removal(L), delete from it all the elements whose indicesare divisible by 3. And return the resulting list after removing unwanted elements.Example:>>>removal(['A', 'B', 'C', 'D', 'E'])['B', 'C','E'Write a function (Ocaml) that takes an ’a list and an int list of values and returns second list, with its integers values replaced by the values from the first vector at the position specified by the integer (indexing starts with 0). Large and negative numbers are to be skipped.
- Does it hold for lists? :Write a function holds_for_lists : ’a list -> ’b list -> (’a -> ’b -> bool) -> bool = that takes an ’a list, an ’b list, a function f: ’ a -> ’b ->bool and returns true if and only if • The two list are of the same length, and • (f a b) is true for all pairs a, b such that a is from the first list, b is from the second list, and a and b appear in the same position in their lists. (oCaml)List of triples or a triple of lists? Write a function l3_of_3l : ’a list * ’b list * ’c list -> (’a * ’b * ’c) list = that transforms a triple of lists into lists of triples. If lengths don’t match then ignore leftover elements. examples l3_of_3l ([1;2;3],[1.;2.],[’a’;’b’;’c’;’d’]);; - : (int * float * char) list = [(1, 1., ’a’); (2, 2., ’b’)] l3_of_3l ([1.;2.],[’a’;’b’;’c’;’d’],[1;2;3]);; - : (float * char * int) list = [(1., ’a’, 1); (2., ’b’, 2)]Write a function(in pyhton) that takes a list of distinct integers l, and an integer k. Your function then finds the index of the integer in l, whose removal from l results in a list whose sum is k. For example, given [3,6,4,1,5,2] and 18, your function should return index 0, which corresponds to 3 in the list. Because, when 3 is removed from the list, the sum of the remaining list [6,4,1,5,2] is 18. You can assume that the given problem is always solvable.
- Write a function merge that merges two lists into one, alternating elements from each list until the end of one of the lists has been reached, then appending the remaining elements of the other list. For example, merging the lists containing A B C and D E F G H should yield the list A D B E C F G H. c++The library function init removes the last element from a non-empty list; for example, init [1,2,3,4,5] = [1,2,3,4]. Show how init could similarly be defined in two different ways.? Explain each definitionThe "outer" list data structure of 2-dimensional lists can be matrix-like ( having same number of elements in each "inner" list or "row"), or it can be ragged (having different number of elements in each "row"). a) Write a Python function called raggs that takes a single argument that is a reference to a 2-d list, and returns the value True if the 2-d list is ragged, and False otherwise. b) Demonstrate that the function works for all relevant cases by inputting different example values.
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