1.Consider the set A def = {{}, {{}}, {{{}}}}. If x∈ A, how many elements might x have?
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1.Consider the set A def = {{}, {{}}, {{{}}}}. If x∈ A, how many elements might x have?
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- Express each set below using the roster method. Write the answer as a set using curly braces. Write all elements in increasing order using commas. Be sure to include the curly braces. Do not include any spaces in your answers. {x € Z+ | a? < 16} {x € Z | x² < 9} {x €N|a? < 9}Consider the function f= {(n,n² – 1) such that n<5,n€N}, written in set-builder notation, which defines a set containing a list of ordered pairs. Write the inverse of f as a set in list form containing ordered pairs. O fl={(0,1),(3,2),(8,3),(15,4)} O fl={(0,– 1),(1,0), (2,3),(3,8),(4,15)} ofl={(1,0), (2,3),(3,8),(4,15)} O fl= {(-1,0),(0,1),(3,2),(8,3),(15,4)} o fl={(3,2),(8,3),(15,4)}Define function p:cat represents set concatenation ◦, which concatenates every pair of strings from both sets using racket. We can specify set concatenation as p1 ◦ p2 = {u · v | u ∈ p1 ∧ v ∈ p2}. Alternatively, we give an inductive specification: ∅ ◦ p2 = ∅ p1 ◦ p2 = prefix(u, p2) ∪ (p'1◦ p2) if p1={u} ∪ p'1.
- Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. +, -, /, * Racket code only please. Thank you!L1 = {u ∈ Σ∗| u ends with aa}.L2 = {u ∈ Σ∗| u ends and begins with different letters }.L3 = {u ∈ Σ∗| u contains abba}.L4 = {u ∈ Σ∗| u is of the form anbamfor n,m > 0}. Given the above languages:(a) Use the set operators ‘union’ and ‘complement’ to describe L5 = L1 ∩ L2.(b) Prove that L5 is regular.(c) Construct an NFA M that accepts L5, and prove its correctness.(d) Convert such NFA (from question above) to a DFA using the algorithm from class.(e) Given the DFA you’ve designed in Q3(d), what is δ(s,au), for u ∈ Σ∗. What is δ(s,buaa), foru ∈ Σ∗. Justify your answers. Note that s is the starting state of the given DFA.Create a set-based implementation of an abstract data type with the following operations. insert(S, x) Insert x into the set S. delete(S, x) Delete x fromthe set S. member(S, x) Return true if x ∈ S, false otherwise. position(S, x) Return the number of elements of S less than x. concatenate(S, T) Set S to the union of S and T, assuming every element in S is smaller than every element of T. All operations on sets with n elements must finish in O(log n) time.
- Given the following sets: U= {1,2,3,4,5,6,7,8,}, A={1,4,5,7}, B= {2,5,6,7,}, and C= {3,4,6,7} Complete the following set operations: a. A U(BUC) b. (A N (B N C))' . c. (A N B) U ( A N C) d. (A N B')U (A N C')Let A-[1.2,3,4), B-(3,4,5,6), and C-(6). Find AN(BUC). Write your answer using set notation, i.e. list all elements separated by comma inside braces) or use the symbol of empty set, if needed Ø. Do not insert any spaces.Q8
- Question 3 Please answer them correctlyLet's assume the deck has n cards and it's cut at m cards. The cut takes the first card off the deck and places it face down, then takes the second card and places it face down on top of the first, and this continues up until and including the mth card. The remainder of the deck, n – m cards, is simply placed on top of the deck of face-down cards. function deck_1(n, m) { // Your code goes here // Return the new location of the // last card which was at offset n-1 return 0; } INPUT: n and m where [n/2] < mSEE MORE QUESTIONSRecommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education