5. Verify if the following are difference sets and state v,b, k, r, A for the ones that are: a) (0,8, 15, 17,20, 21) (mod 31). b) (1, 5,7, 8 ,9, 11,16,18) in Z19- c) (0, 1,2.4,5,8,10) in Z15.

Q: Prove the following set infinite: {5,9,13,17,...}

A:

Q: prove that any set S subset of {1,2,,...100} with |S|=26 contains at least one odd number or it…

A: We have a subset S of {1,2,.......,100} with |S| = 26. We have to prove that S contains at least one…

Q: 5. Verify if the following are difference sets and state v, b, k, r, A for the ones that are: a)…

A: 5(a) Given that, (0,8,15,17,20,21)mod31 The cardinality of the set is 6 with mod31. Here V is the…

Q: Suppose you have 6 black and 9 white t-shirts and you dont want to put black ones on top of another…

A:

Q: 10 What is the preimage of (3, 5) under the translation (x, y) (x-4, y + 6)? O (7, -1) O (1, 1) O(1,…

A:

Q: Hamilton circuit

A:

Q: 7. There is a SUNY-Korea party that n men and n women attended. Each ma knows exactly k women, and…

A: Men n Women m   Each woman knows exactly    k women k men Bipartite graph

Q: How many ways are there to assign 100 different diplomats to five different conti- nents if 10…

A: Here,  total diplomats = 100 Number of continents= 5 Also, in continent 1, 2 ,3,4,5 there sholud be…

Q: Let S={rEZx+3=5(mod 17)}. Then S is

A: We will solve these questions

Q: 4 Prove that סלא is Riomonn inkgpable

A:

Q: 2,2 and write tte answers in the comepute form of atib s 2.

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

Q: Given that 7,=21+)i and Za= FatYai Prove that

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let S = {25, 30, 35, ... , 280, 285, 290}. That is, it consists of the multiples of 5 from %3D 25 to…

A:

Q: 1. Will there be at least two people who celebrate their birthday on the same day Yes, definitely O…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: 2. Let, a, = 3, az = 4 and for n 2 3, a, = 2a,-1 + an-2+ 5, express a, in terms of n.

A: Topic:- series sum

Q: Suppose A₁, A2, ..., A30 are thirty sets each having 5 elements and B₁, B₂, ..., B₁ are n sets each…

A: Given that A1, A2, . . ., A30 are thirty sets each having 5 elements and B1, B2, . . ., Bn  are 'n'…

Q: 1. Out of 120 people, it was found that 50 like pasta, 42 like pizza, 39 like burger , 21 like pasta…

A:

Q: SUppose K,n EZ and O < Kcn. Prove +hat by (onsi nsi dering subsets of (1,... --- --- (^) - (":') + (…

A: The given problem is to prove the following identity using the basic mathematical identities.

Q: Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}U={1,2,3,4,5,6,7,8,9,10}. Express each of…

A: To represent the given sets in terms of binary strings (of length 10)

Q: Show that the Post Correspondence Problem is decidable over the unary alphabet S = {1}.

A: To Prove :- The Post Correspondence Problem is decidable over the unary alphabet S =1.

Q: 1. Let, a, = 3, az = 4 and for n 3, a, = 2a,-1+ an-2, express a, in terms of n.

A:

Q: Suppose A1, A2, ..., 430 are thirty sets each having 5 elements and B₁, B2, ..., B₁ are n sets each…

A:

Q: 8. Determine for which n > 3, W, has a Hamilton circuit. Justify your answer. 72

A:

Q: 1 1 1 1) Show that с 3(6 -а)(с-а)(с-b) а a? b? c?

A:

Q: From the letters {A, B, C, D, E, F. G}, how :many 3-distinct-letters codes can be (a) generated? (b)…

A: a) 7C3 distinct codes can be generated by {A,B,C,D,E,F,G} which is equal to 21

Q: Let $S = \{25, 30, 35, \dots, 280, 285, 290\}$. That is, it consists of the multiples of 5 from 25…

A: We have S=25 , 30, ...., 290 Now, the first element in the set is 25 and the last element is 290.…

Q: Suppose that in a certain state, all automobile license plates have three uppercase letters followed…

A: There are 26 letters [A-Z] and 10 digits [0-9] d) If the letters and digits are distinct then we can…

Q: Assume that product codes are formed from the letters T, Z, Q, V, Y, U, and X, and consist of 6 not…

A: To determine the total number of product codes satisfying different specified conditions

Q: Let x, y E N, determine each of following statemen is true or false (N means Natural number, natural…

A:

Q: 8. Convert the set X in roster form if set X contains multiples of 5 which is less than 50.…

A: Roster notation of a set is a simple mathematical representation of the set in mathematical form. In…

Q: 5- Determine whether each of the following is singular or nonsingular: [4 1 -2] i- A=1 7 3 5 8 [3 2…

A: A square matrix of size n x n is non singular if det(A) is not zero and singular if det(A) = 0

Q: EX Find theno of letter strings of length H that contain the letter y exactly 3-himes and contain…

A: Total number of letters = 26 Letter y can occur only thrice. Letters m,b,t,k can occur only once.…

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: Let S(a, b) = {na + mb : n, m ∈ Z}. For any a and b in Z, not both zero, the set S(a,b) is precisely…

A: Take the set S={ax+by&gt;0:x,y∈Z} Without loss of generality, assume that a&lt;b. Then b−a&gt;0 is…

Q: Let $\quad U=\{1,3,5,7,9,11,13\}, \quad A=\{1,3,5,7,9,11\}, \quad B=\{1,3,7,9\}$,$C=\{3,9,11\},$ and…

A: U=1, 3, 5, 7, 9, 11, 13A=1, 3, 5, 7, 9, 11B=1, 3, 7, 9C=3, 9, 11D=1, 9

Q: a) Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of these sets…

A:

Q: 11. Suppose the universal set contains the natural numbers that are no more than 20. Sets A and B…

A: 11 Suppose the universal set contains the natural numbers that are no more than20. Sets A and B are…

Q: 15 Assume that set S has 11 elements. How many subsets of S have at most 2 elements?

A: Solution : A set S has 11 elements We want to find subset of S have at most 2 elements

Q: Suppose that X, Y are subset of U. If Pr(X)= 0.35, Pr(Y)= 0.36, and Pr (X intersect Y)= 0.09, what…

A: Given Suppose that X, Y are subset of U. If Pr(X)= 0.35, Pr(Y)= 0.36, and Pr (X intersect Y)= 0.09

Q: A math tutor working with a small study group has classified students in the group by whether or not…

A:

Q: Assume that X={A,F,H,D,C} and Y={5,9,4,2,3}. A code consists of 4 different symbols selected from X…

A:

Q: Write down all even permutations of {1,2,3,4} which take the element 1 to 2.

A: To write all even permutation of A={1, 2, 3, 4} that takes 1 to 2.

Q: if it was a bez Prove that لما لها حاطها

A:

Q: prove that (1, 6) 13 an o pen set 13 an open çet.

A:

Q: Let S = {25, 30, 35, ., 280, 285, 290}. That is, it consists of the multiples of 5 from .... 25 to…

A: Given that the set S={25,30,35,....,280,285,290} which consists of multiple of 5 from 25 to 290. We…

Q: Suppose you have 6 black and 9 white t-shirts and you dont want to put black ones on top of another…

A:

Q: ) Suppose in a university, each subject offered to students has a subject code consisting of four…

A: Permutation is a technique to obtain the possible arrangements of listed items in linear order. It…

Q: Assume that A = { 1, 3, 5, 8, 9}and that U = set of natural numbers less than 11. Find A'. * O {2,…

A:

Q: Set us the matrix of transition probabilities and show the transition b. Find the steady state…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.