3. Is (S, R) a poset if S is the set of all people in the world and (a, b) ≤ R, where a and b are people, if a) a is taller than b? b) a is not taller than b? c) a = b or a is an ancestor of b? d) a and b have a common friend?
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- Define X union Y. How is the union of X and Y denoted? Define X intersect Y. How is the intersection of X and Y denoted Define X and Y are disjoint sets. Define the difference of sets X and Y. How is the difference denoted What is a universal set? What is the complement of the set X? How is it denoted? Define symmetric difference of X and Y. How is the symmetric difference denoted? Draw a Venn diagram for all set operations above.Answer itthe nfa. 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.?If A = {}, Discuss briefly using significant words why set A is an empty set…
- 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.In the following problems ((f) - (j)) you are given the description of a set. Your task is to write down the set in the formal language of set theory by specifying the membership condition of the set. There are many possible answers here, but make sure that the condition you specify actually determines which elements belong to that set. (h) Assume the numbers in this set are natural numbers N. {0, 10, 20, 30, 40, 50, . . . } (i) Ecin U (j) The intersection of Ecin U and F.1- consider the following implementation of double linked list class. public class DLIST<E> { static class Node<E>{ private E data, Node<E> next, Node<E> prev; private Node(E dataItem, Node<E> nextnode, Node<E> prevnode){ // constructor data = dataItem; next = nextnode; prev = prevnode } private Node(E dataItem) { //constructor data = dataItem; next = null; prev=null; } } private Node<E> head=null; private Node<E> tail=null; //initialisation } a) Write a Java method that prints 1st, 3rd, 5th, etc. nodes in the double linked list. b) Write a java method to display the double linked list in the reverse 2-Quick Sort is one of the fastest sorting algorithms in Computer Science. a) Write the quick sort algorithm. b) Sort the following array using the QuickSort algorithm (Assume the first element as the pivotal element).…
- a discrete probability distribution sampling. Create a class called Sample that supports the following two operations and has a function Object() { [native code] } that accepts an array p[] of double values as an argument. Change(i, v) changes the value of p[i] to v and random() returns an index I with a probability of p[i]/T (where T is the sum of the numbers in p[]). Use a full binary tree with implied weights of p[i] at each node. The total weight of all the nodes in a subtree should be stored in each node. Choose a random number between 0 and T to create a random index, and then use the cumulative weights to decide which branch of the subtree to explore. Change each node's weight along the path from the root when modifying p[i].Find the most general unifier (if it exists): a) Marries (x, John), Marries (Elizabeth, y) b) Marries (thatperson, Mary), Marries (father (Me), mother (y))Question 1:Convert a decimal to binary and binary to decimal using recursionTest your implementation with following examples:● (1947)10 = (11110011011)2● (1992)10 = (11111001000)2● (2021)10 = (11111100101)2Question 2:Implement a member function that prints a singly linked list in reverse order without creating acopy or changing the original List.void printBackwards() constQuestion 3:Implement a recursive member function “isSorted” which recursively checks whether the linked listis sorted (ascendingly).bool isSorted() constQuestion 4:You will implement a function bool Equalize_Occurrences (char key, int maxcount) of theclass list, that will take a character key and maximum count for the consecutive occurrences of thekey inparameters. It will then traverse the list, verify and update the consecutive occurrences of the keyaccordingto maximum count and returns true. It returns false if no occurrence of key is found.Note: You can traverse the list only once for this task.
- Draw ALL the possible parse trees for (p → ¬q → q) → (p → q), without assuming any binding priorities of the connectives. ( 3 trees) There are three different trees please draw them all.Which of the following best illustrates the concept of polymorphism? Why? That a) and b) have different answers. That e) and f) have different answers. That k) and l) have different answers.Don't post plagarism Evaluate the two approaches for supporting dynamic allocation and deallocation for dynamic length strings.