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Discrete Math

Discrete Math : Functionally Complete

6. a) What does it mean for a set of operators to be functionally complete? b) Is the set {+, .} functionally complete? c) Are there sets of single operator that are functionally complete? Please see the attached file for the fully formatted problems.

Rules of Inference, Logic and Symbology

Designate each simple statement with a letter. Then write down the compound statements using the following rules(modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, addition, simplification, or resolution), arrive at the conclusion. I've done all but the latter. If you send an email then I will write t

Discrete math proofs

(See attached file for full problem description with proper symbols and equations) --- 1)Prove that for any non-empty sets A x (B-C) = (AxB)-(AxC) 2) Let a,b be integers and m a positive integer. Prove that: ab = [(a mod m ) * (b mod m) mod m ] 3)Prove or disprove (a mod m) + (b mod m) = (a+b) mod m for all intege

Discrete Mathematics and its Applications : Greedy Algorithms

Greedy Algorithms procedure change (c1, c2, ...., cr: values of denominations of coins, where c1 > c2 > ... > cr; n: a positive integer) for i : = 1 to r while n ≥ ci begin add a coin with value ci to the change n :=n - ci end 2. Use the greedy algorithm to make change using quarters, dimes, ni

Discrete Mathematics and its Applications : Greatest Common Divisors

A) Define the greatest common divisor of two integers. b) Describe at least three different ways to find the greatest common divisor of two integers. c) Find the greatest common divisor of 1,234,567 and 7,654,321. d) Find the greatest common divisor of 2335577911 and 2937557313. Please see the attached file for the fully f

Discrete Mathematics and its Applications - Sets and logic

For each topic demonstrate a knowledge and capability by giving the following information: 1) Problem Solution: (solution for an even number problem) See below... 2) Personal Observation: (personal comment on the topic including advice to others on how to study and understand it). Logic 10. Let p, q, and r be the prop

Set Theory Proof : Inclusion-Exclusion Principle

3. This exercise is about the inclusion-exclusion principle. a) Let X and Y be finite ts and suppose that |X| = 11, |Y| = 6, and |X∩Y| =4. Find |XUY|. b) Suppose that U is a finite universal set. If |U| = 21, |XUY| = 11. |X| = 4 and |Y|= 10. find |XcUYc|. c) Each tile in a collection of 19 is a square or a triangle and

Dynamic Programming : Write an Algorithm to Minimize Cost

There are n trading posts along a river. At any of the posts you can rent a canoe to be returned at any other post downstream. (It is next to impossible to paddle against the current.) For each possible departure point i and each possible arrival point j the cost of a rental from i to j is known. However, it can happen that


Let T[1..n] be a sorted array of distinct integers, some of which may be negative. Give an algorithm that can find an index i such that 1 <= i <= n and T[i] = i, provided such an index exists. Your algorithm should take a time in Big "O" (log n) in worst case.

5 Finite Math Problems

1) A man walking in the woods encounters a stream. Because he is unsure of the stream depth, he measures how deep the water is in many random spots along the entire width of the stream. After 1000 measurements each with a depth of 6 inches, he concludes the probability of the water being 6 inches deep the entire way across to

Finite Math

1.) Dan borrows $500 at 9% per annum simple interest for 1 year and 2 months. What is the interest charged, and what is the amount due? ________________________________________ 2.) A mutual fund pays 9% per annum compounded monthly. How much should I invest now so that 2 years from now I will have $100 in the account?

Finite Math

(See attached file for full problem description) --- 1. What is marginal cost? Fixed cost? Find the slope for each line that has a slope. 3. Through (-2, 5) and (4, 7) 5. Through the origin (11, -2) 7. 2x + 3y = 15 9. y + 4 = 9 11. y = -3x Find an equation in the form y = mx + b (where possible) for each line.

Finding a lighter or heavier ball out of 12 balls

You have 12 balls out of which one is odd ie lighter or heavier than others. You can't identify the odd ball just by looking at it. So, how you would find out the ball, using the weighing scale and maximum weighings allowed are three only?

Finite Mathematics - 20 Review Questions

Please see the attachment. Problems 1-3 (also attached): Acme Inc. has just purchased new computers for $60,000. Suppose that in 8 years the computers will have a salvage value of $8,000. The college plans to depreciate the value of the computers linearly over the 8 years. 1. Based on the above information, value

Bijections, Denumerability, Tautologies, Sets, Logic and Proofs

Consider the compound statement (P ^ Q) V (~ P ^ R) a) Find the truth table for the statement. b) IS the statement a tautology? c) In the following program code, what has to be the output for the answr to be "yes"? ... 2. Given the following sets A = {1.2,3.4}, B = {2,3,4,5}, and C= {2,4,6} a) Find .... 4. Prove that

Logic and Logistics : Crossing a Desert and Supply Chain

This is a workbook example called crossing a desert. Suppose you and your truck are all set to leave the town of Ucnestahn on the edge of Ucnahara desert. you want to travel across the desert as quickly as possible. You have calculated that all the provisions you need for one day's travel (food, fuel, lager, chewing gum, 'w

Abelian groups

Let G ---> H be a group homomorphism and... Show that if... then &#934;[G] is albelian. Please see attached for full question.


*1.In a multiple regression model, the value of the coefficient of multiple determination a. has to fall between -1 and +1. b. has to fall between 0 and +1. c. has to fall between -1 and 0. d. can fall between any pair of real numbers. *2.A medical doctor is involved in a $1 million malpractice suit. He can either settl

Business Statistic and Finite Math

1.If a categorical independent variable contains 2 categories, then _________ dummy variable(s) will be needed to uniquely represent these categories. a. 1 b. 2 c. 3 d. 4 2. A dummy variable is used as an independent variable in a regression model when a. the variable involved is numerical. b. the variable involved is

Finite math/business analysis- Multiple choice questions on statistics

1.A recent survey of frozen convenience meals found a correlation of r = 0.768 between calories and fat content in the sampled meals. Which of the following is the most appropriate conclusion from this survey about the relationship between calories and fat content? a. Higher fat content in the sampled meals resulted in a h

Venn Diagram From a Table

The Wilcox fam is considering buying a dog. They have established several criteria for the family dog; It must be one of the breeds listed in the table, must not shed, must be less than 16 in tall, and must be good with children. a.) Using the information in the table, construct a Venn diagram in which the universal set is

Game Theory Problem

Rose and Cathy decide to play a matrix game. Each has two options, conveniently called W and L. If both pick W, Cathy pays Rose $4; if both pick L, Cathy pays Rose $2; if Rose chooses L and Cathy chooses W, Cathy pays $1 to Rose; and finally, if Rose chooses W and Cathy chooses L, Rose pays Cathy $1. The payoff matrix for Rose