A = {a, ab, aab}, A set of strings over the alphabet (a, b). For strings, we have an interesting notation to define the universal set U in this context. We take U defined by the Kleene closure (*) of the alphabet: U = {a,b}* = {a,b)}¹ = {a,b}° U {a,b}¹ U {a,b}² U... (20 Answer the following questions. a) What is the shortest string in the universe for A? b) How many strings are contained in A? c) Write the contents of {a, b}° U {a,b}¹ U {a, b}² in roster notation.

Let ∑ = {a, b}. Given the language L = {b^n a^m: m,n≥0}, find the regular expression r such that L(r) = L.

Consider a set P of points in the plane. Each point is given as a list of two elements [x,y], where x and y are integers. The set Pis given as apython list of points. For example P = [[1,2] , [2,6] , [3,3], [6,1], [2,2]]. A point [x,y] is a super point of P if there does not exist another point [u,v] in P with u > x AND v > y. Define a function (procedure) called super () that takes one parameter, which is a set of points as de- scribed above, and modifies the point set (python list) by removing all elements which represent points that are not super. This function should not include a return statement. After running super (P), the el- ements remaining in P should be in their original order. For example, after running super () then P = [[2,6], [3,3], [6,1]].

Given a list of rational numbers,find their product. ConceptThe reduce() function applies a function of two arguments cumulatively on a list of objects in succession from left to right to reduce it to one value. Say you have a list, say [1,2,3] and you have to find its sum. >>>reduce(lambdax,y:x+y,[1,2,3])6 You can also define an initial value. If it is specified, the function will assume initial value as the value given, and then reduce. It is equivalent to adding the initial value at the beginning of the list. For example: >>>reduce(lambdax,y:x+y,[1,2,3],-3)3>>>fromfractionsimportgcd>>>reduce(gcd,[2,4,8],3)1 Input Format First line contains , the number of rational numbers.The  of next  lines contain two integers each, the numerator(  ) and denominator(  ) of the  rational number in the list. Constraints     Output Format Print only one line containing the numerator and denominator of the product of the numbers in the list…

Let Σ={0,1}. Give a regular expression r over Σ such that L(r) = { w in Σ* | (w contains at least 2 symbols, that is, the length of w is at least 2) and (the first symbol of w is different from the last symbol of w) and (centre (w) is mimsy according to the following two definitions)}. For any string y containing at least 2 symbols, let centre (y) be the substring of y obtained by removing the first symbol and the last symbol of y. A string x over Σ is called mimsy if x is made up of either • at least two 0-symbols (and no 1-symbols), or an even number of 1-symbols (and no 0-symbols).

Find all strings in L(ba + ab*a) of length less than four. Find a regular expression for the set { a" bm : n, m are even}.

Let E= {0,1}. Give a regular expression r over Σ such that L(r) = { w in Σ* | (w contains at least 2 symbols, that is, the length of w is at least 2) and (the first symbol of w is different from the last symbol of w) and (centre (w) is mimsy according to the following two definitions)}. For any string y containing at least 2 symbols, let centre (y) be the substring of y obtained by removing the first symbol and the last symbol of y. A string x over Σ is called mimsy if x is made up of either • at least two 0-symbols (and no 1-symbols), or • an even number of 1-symbols (and no 0-symbols).