Let U = {a1, a2, a3, ... , an, b1, b2, b3, ..., bm, C1, C2, C3, .. Cx} be a set roster of elements in universe U with subsets A, B, C and let R denote an equivalence relation with equivalence %3D classes [A] = Vn(an E A), [B] = Vm(bm E B), [C] = vk(ck € C). %3D %3D a) What would we expect to be true about [A] n [B] , [B]n [C], and [A] N [C]? b) Thinking about your response to the previous question, suppose it was found during an analysis of the elements of U that c; E A, for some i E N. Would [A] = [C] return True or return False? How do you know? ==

Q: Given the classical sets A = {9,5,6,8,10}, B = {1,2,3,4,7,9} and C = {1,0}, define on universe X =…

A: According to answering policy we can answer only 1st question. For remaining questions you can…

Q: Problem 1 Rank the following functions by order of growth; that is, find an arrangement g, g2, . ..…

A: It is defined as a set of functions whose asymptotic growth behavior is considered equivalent. For…

Q: 3. Consider the following NFA. The set of states, Q, is {1,2,3}. The initial state is 1 and the ac-…

A: Converts NFA to DFA- The following steps are followed to convert a given NFA into a DFA- Step-01:…

Q: Consider the relation R defined on the set Z x Z: R = {((a,b),(c,d)) | a = c (mod 4) a b = d (mod…

A: given that

Q: An integer X is cool if it has a primitive root modulo X. The coolness of a non-empty set of N…

A: Here is the detailed and simplified C++ code for the above listed problem statement:

Q: Sereja likes to hang around trees. A tree is an undirected graph on N vertices with N-1 edges and no…

A: Given:

Q: 1. The subset sum problem is stated as follows: Given a set S {a, a, a, a,} of n positive integers…

A: A naive solution would be to cycle through all the subset of n numbers and, for every one of them,…

Q: Sets 1. Let A, B, C C U be subsets of some universe U. Let S = [(AN B) \ C]U[(AnC)\ B]U [(BnC) \ A].…

A: Answer S contains all the elements which are contained in exactly two subsets, i.e. if x is an…

Q: Determine whether each of the following sets is unifiable. If yes, obtain a most general unifier. w…

A: so here we have to find the given set are unifiable or not

Q: Given set A = {a, b, c, d} show the equivalence relation, which contains eight ordered pairs,…

A: Answer is in step 2

Q: Consider the following set of ordered pairs of the elements of a set A = {1,2, 3, 4} of numbers and…

A: Answer: This is a map from A to C and is one-to-one

Q: 2. Show that the following languages are in NP, by providing a non-deterministic algorithm. You are…

A: A=<G,K>|G is K-colorable Answer: In undirected graph G k-coloring  is an assignment of colors…

Q: Suppose we wanted to show that if Sis a finite set, then |2| = 2SI (where 2 is another way of…

A: Suppose we wanted to show that if S is a finite set, then |251 = 215 (where 25 is another way of…

Q: Let A be the following set of discrete functions: A {3n2 + log n, 5n log n, 4", n", n! + log n, 3" +…

A:

Q: 4.3. The fuzzy sets A. B. and C are all defined on the universe X = [0, 5] with the following…

A: Solution:-

Q: Consider the set F = {1, −1, i, −i} with an operation ✕ defined by the table. ✕ 1 −1 i −i 1 1 −1…

A: Given Data : Table of operations : X 1 -1 i -i 1 1 -1 i -i -1 -1 1 -i i i i -i -1 1 -i -i…

Q: is an ordered * .collection of objects relation O set non of them O O O

A: A relation is a collection of ordered pairs containing one object from each set. So option a is…

Q: i. Let S ⊆ ATM. What do the elements of S look like ? e.g. “An element of S is a pair such that ”.…

A: Let S ⊆ ATM. What do the elements of S look like ? If all elements of S are also elements of ATM…

Q: Sereja likes to hang around trees. A tree is an undirected graph on N vertices with N-1 edges and no…

A: The above question given an array of N elements, and that let F(C) be the number of the different…

Q: Let A1, A2,..., An CU be n subsets of some universe U satisfying that A1 Ç A2 Ç A3 Ç .… Ç An. Prove…

A: The handwritten answer is to be solved below:

Q: Let R(A, B, C, D, E) be a relation with the set of FD's: F = {D → C, C → D, D →A, C –→ A, E → C, E…

A: To find the canonical cover of F find the closures of left hand side variables we have F={…

Q: Let R = (J,K, L, M, N, P) and F = {J → KL, L → J, MNP → K, KP – M, LJ → N}, give a canonical cover…

A: As per guideline, I can do only first one. Please re-post pending question in next post. I hope you…

Q: In the setting of the previous question, suppose our disjoint set data structure uses the…

A: 1. Merged list is f 2. Merged list is b 3. Merged list is d 4. Merged list is e 5.Merged list is c…

Q: Let A equal the set of all strings of 0's, 1's, and 2's that have length 4 and for which the sum of…

A: A = { 0000, 1000, 0100, 0010, 0001,            1100, 1010,  1001, 0110, 0101,            0011, 2000,…

Q: Assume we want to perform k-Nearest Neighbor classification to find the class of an unknown point in…

A: Solution: Now, we will calculate the distance of the unknown point i.e, (0,0) from the points given…

Q: Consider the following set of ordered pairs of the elements of a set A = {1,2, 3, 4} of numbers and…

A: Explanation:- 1) It is map from A to B 2) it is one to one because there is no repetition of…

Q: Consider a set x composed of 2 level height binary trees. We define a relation R if two given…

A: Solution :-   R is an equivalence relation, to be sure. [0], [1], [2], [3], [4], [5], [6], [7], [8],…

Q: O be the set of odd numbers and O’ = {1, 5, 9, 13, 17, ...} be its subset. Define the bijections, f…

A: A) The answer is an given below :

Q: An integer X is cool if it has a primitive root modulo X. The coolness of a non-empty set of N…

A: Example Input 3 3 4 1 2 1 10 15 20 1 8 1 8 Example Output 10 0 1703   Code in C++ is given below :…

Q: Let T be a DFS tree, u and v nodes in T, and (u,v) an edge in the graph G that does not exist in T.…

A: [ Note: In question, you didn't mention a Directed or Indirect graph, so I have given the…

Q: Q4. Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly?

A: Here we have given a solution for the given set A that satisfies A = {A}

Q: use an element ove the statemenit. (Assumme that ail sets are subsets of universai Set Statement:…

A:

Q: Sereja likes to hang around trees. A tree is an undirected graph on N vertices with N-1 edges and no…

A: Please find the below Java CODE:

Q: 12. Suppose C is a class of subsets of 2 and suppose BC satisfies B e o(C). Show that there exists a…

A: let 'G' be the union of all σ-algebras generated by countable subsets of CB.

Q: (b) Analyze a system that is composed of the sets Process (P), Resource (R), and Edges (E) where: P…

A: The answer is

Q: Sereja likes to hang around trees. A tree is an undirected graph on N vertices with N-1 edges and no…

A: The above question given an array of N elements, and that let F(C) be the number of the different…

Q: Suppose that relations R and S have n tuples and m tuples respectively. What is the minimum number…

A:

Q: Consider the formula B = 3x3y3z. p(x,y) p(x, z) ^ ¬p(y, z). For each of the following…

A: Hey there, I am writing the required solution for the above stated question.

Q: Show that property (3) of a matroid implies: For any S ∈ I, {x} ∈ I, there exists y ∈ S, such that S…

A: The answer as follows

Q: 4.1. Two fuzzy sets A and B, both defined on X, are as follows: µ(x;) x1 x2 x3 tx X5 X6 A 0.1 0.7…

A: According to the Bartelby guidelines we are suppose to answer only 3 sub part of the question.…

Q: Consider the array t = [1, 2, 3, 4, 5, 8, 0 , 7, 6] of size n = 9, . a) Draw the complete tree…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Show by membership that for all sets A, B and C: AU (B – A) C AUB

A: Assume, A= {1,2,3,4,5} B= {6,7,8}

Q: ng equiva R = {(1,1), (1,5), (2,2), (2,3), (2,6), (3,2), (3,3), (3,6), (4,4), (5,1), (5,5), (6,2),…

A: A={1, 2,3,4,5,6} Given the equivalence relation R on A is {(1, 1), (1, 5), (2, 2), (2, 3), (2, 6),…

Q: Suppose that relations R and S have n tuples and m tuples respectively. What is the minimum number…

A:

Q: 6. () For classes of P, NP, and NPC, assuming PNP, which of the following is true? Explain each why…

A:

Q: 4.3. The fuzzy sets A, B, and C are all defined on the universe X = [0, 5] with the following…

A:

Q: Let A = {x, y} ; B = {1,2,3}; and C = {a, b}, then `A B×C=.. إجابتك Let A and B be two sets. We say…

A:

Q: pAp Consider the partal order on the set X(a. b.c.d.e.1)with the following relations aくも くe もくe もく。…

A: Given set is, X={a, b, c, d, e, f} Given partial order sets are: a<=b, a<=c, b<=c, b<=d,…

Q: |{1,1}x{2,3,4}| is : * O 5 O 6 O 4 Consider the sets: A = %3D {1,3,4,5,8,9} B = {1,2,3,5,7} and C…

A: Solution: