### Logic : Sets

Find A U B where A= {x | x is an even integer greater than 3} B = {x | x is an odd integer greater than 10}

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Find A U B where A= {x | x is an even integer greater than 3} B = {x | x is an odd integer greater than 10}

Construct a truth table for the statement below: p^(~pVq) Is the statement a tautology?

1. Find the maximum flow and the associated minimum capacity cut for the following network, by using flow augmenting path algorithm (in the order of "first labeled, first scannred"). *see attachment for diagram* 2. A maximum capacity flow augmenting path is an augmenting path such that we can increase the flow of the network

Question 1. Translate each of the following statements into the notation of logic and predicate logic and simplify the negations of all. Which statements do you think are true? (i) Some questions are easy. (ii) Any integer with an even square is even. (iii) All students cannot correctly answer some questions in this assignme

Geometry Finite Axiomatic Geometry Finite Axiomatic Geometry This abstract geometry confuses me and I just can't follow this logic. Here is a set up of the question. P

Letting x,y be elements of the real numbers, prove that |xy|=|x||y|.

Use the information provided: U={1,5,10,15,20,25,30} A={1,10,15} B={1,10,20,25} C={5,15,30} and use a venn diagram to determine wheather (A U B') U C= (A' U B) U C' for all sets A, B, and C. Show your work.

The Action Sports Network surveyed 265 of its viewers to determine which sports they watched most often. The results of the survey showed: 140 viewers watched football 130 viewers watched baseball 120 viewers watched hockey 60 viewers watched football and baseball 55 viewers watched baseball and hockey 50 viewers watche

For each of the following properties, find a binary relation R such that R has that property but R^2 (R squared) does not: (a) irreflexive (b) antisymmetric

I would appreciate it if someone could provide the solutions to QB5 of the attatched exam paper. Please see the attached file for the fully formatted problems. B5. (a) (1) State and prove the Chinese Remainder Theorem. (ii) Find the 2 smallest positive integer solutions of the simultaneous set of congruence equations: 2x

What are random variables?

Please see the attached file for the fully formatted problems. Verify DeMorgan's laws (equation 1 and 2 below) using truth tables. Prove the generalized DeMorgan's laws: (1) (NOT(p1 p2 .... pk)) (2) (NOT(p1+p2+...+pk)) by induction on k, using the basic laws: NOT(pq) NOT(p+q) Then, justify the ge

Can anybody explain and summarize the detail of John Nash's paper please? It is in the attachment file.

The Chinese Remainder Theorem (CRT) applies when the moduli ni in the system of equations x≡ a1 (mod n1) ... x≡ ar (mod nr) are pairwise relatively prime. When they are not, solutions x may or may not exist. However, the related homogeneous system (2'), in which all ai=0, always has a solution, namely the trivial

Let a be an integer. Prove that 2a + 1 and a^2+ 1 are relatively prime. ( relative primes are numbers that their largest common divisor is 1). ONLY RESPOND IF THERE IS A a. mistake b. something is unclear c. proof is correct, but solved incorrectly (does not follow instructions) Exm. Instruction says proof by inducti

Take an in-depth look into this proof. Obviously it is wrong. Where is it wrong and why? This is obviously wrong. Where and why? Detailed explanation is needed of where and why it is wrong with all examples. Thanks Let a = b. Multiply both sides by a (OK because we don't violate the equal sign). We get a² = ab. Subtrac

At the start of the year, a company wants to invest excess cash in one-month, three-month and six-month Certificates of Deposit (CD's). (Purchase price and yields for the different CD's appear in the table below). The company is somewhat conservative, however, and wants to make sure that it has a safety margin of cash-on-hand e

I need assistance with following problem along with steps to arrive at the solution/answer. Three envelopes are addressed for 3 secret letters written in invisible ink. A secretary randomly places each of the letters in an envelope and mails them. What is the probability that at least 1 person receives the correct letter?

The problem I am working is the following; please provide step-by-step to obtain solution's. I am unable to figure (c) out the ANSWER IS ... 7805 There are 5 rotten plums in a crate of 25 plums, How many samples of 4 of the 25 plums contain at least one rotten plum?

We can define sorted lists of integers as follows: Basis - A list consisting of a single integer is sorted. Induction - If L is a sorted list in which the last element is a and if b >= a, then L followed by b is a sorted list. Prove that this recursive definition of "sorted list" is equivalent to our original, nonrecurs

A. Write 3n − (k + 5) in prefix notation: ????. b. If T is a binary tree with 100 vertices, its minimum height is ????. c. Every full binary tree with 50 leaves has ???? vertices.

I have done several examples but these I cannot get right, I am not sure where I have made the mistake and I am confusing myself. a. List all the binary relations on the set {0,1}. b. List the reflexive relations on the set {0,1}. c. List the symmetric relations on the set {0,1}.

Write in prefix and infix notation: x 2 w + yz * -1

A. Use the definition of big-oh to prove that 3n - 8 - 4n^3 / 2n - 1 is O(n^2). B. Use the definition of big-oh to prove that 1 . 2 + 2 . 3 + 3 . 4 + ... + (n - 1) . n is O(n3).

For each case, think of a set S and a binary relation p on S for - A. p is reflexive and symmetric but not transitive b. p is reflexive and transitive but not symmetric c. p is reflexive but neither symmetric nor transitive

Characterize the set of all real numbers with the discrete metric as to whether it is compact, complete, or totally bounded. Use definitions only! (i.e. compact => every sequence converges, etc)

Prove: any subgroup of the order of p^(n-1) in a group of order p^n, where p is a prime, is a normal subgroup

The following is is meant to have some assumptions made (like "n"). I have been up all night trying to figure this out. It can't be Euler because the vertices can't be >1. It might be Hamilton if I assume that E of G(V,E) is infinte..but how would I get my answer? I would just have sets (e1, e2,...) Could this be a straight

Determine whether the binary relation R on Z, where aRb means a^2 = b^2, is reflexive, symmetric, antisymmetric, and/or transitive.

Find the value and the optimal strategies for the two person zero-sum game below. Player 2 Player 1 1 2 3 2 0 3 I have determined the value of the game, but I don't know how to get to the optimal strategy. Please step through. My professor gave us the answer: Row Player Value = 4/3, The optimal strategy for the ro