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# Discrete Math

### Removable singularity

(See attached file for full problem description) --- Let have an isolated singularity at and suppose that is bounded in some punctured neighborhood of . Prove directly from the integral formula for the Laurent coefficients that for all j = 1,2,3,..., i.e. must have a removable singularity at . The integ

### 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.

### Numerical Methods Proofs

a) Show that the l_inf vector norm satisfies the three properties i. ||x|| > 0 if x =/ 0 and x belongs to R^n ii. ||lambda(x)|| |lambda| ||x|| if lambda belongs to R and x belongs to R^n iii. ||x + y|| <= ||x|| + ||y|| for x, y belonging to R^n. b) consider the matrix 4 2 1 A = 2 5 -2 1 -

### Finite or Countable Collection

a) If {I } is a finite or countable collection of disjoint open intervals with I (a, b), Prove that (m: Measure). b) If U (empty set) is an open set of R, Prove That (U)> 0. c) Let P denote the cantor set in [0, 1]. Prove that m(P) = 0. d) Suppose that U, V are open subsets of R, a,b R with U [a,b] = V [a,

### 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

### Mid Span Deflection : Transposing Equations and Solving by Substitution

The equation for the mid-span deflection of a simply supported beam carring a uniformly distributed load can be determined from. M=5WL^3 / 384EI AND I=bd^3 / 12 where: M = mid-span deflection W = total load L = span E = Young's modulus of elasticity I =

### 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

### Partially ordered set Proof

A set A is call a partially-ordered set if there is a relation R on A such that R is reflexive and transitive. If A is any set, prove that the power set P(A) is a partially ordered set under the relation "is a subset of".

### 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

### Jacobi and Legendre Symbols and Proofs

1. Prove that if b and c are odd, then (a/bc)=(a/b)(a/c) 2. Prove that if a==b (mod c), where c is odd, then (a/c)=(b/c)

### 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

### 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}

### Proofs of least upper bounds

1. If supS=a and X={s-k l s element of S}. Prove that supX = a-k 2. If A and B have least upper bounds, prove sup(AUB) = max(supA, supB) 3. Prove for all x<supS there exists y that is an element of S such that x<y< or = supS.

### Detailed Explanation to truth table

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

### Flow Augmenting Path Algorithm, Bipartite Graph and Cardinality

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

### Math Symbols, Logic, Predicate Logic and Simplification

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

### Finite Axiomatic Geometry

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

### Group Proofs : Properties of Groups

Let G be a group. x and y are elements of G. Prove that: a. The inverse of xy is y^-1x^-1 b. The identity element, e, is unique c. The inverse of any element x of G is unique d. If xy = xz then y = z e. If x^-1y^-1=y^-1x^-1 then xy = yx f. If every element x of G satisfies x x = e, then for any two elements, x, y,

### Proof : Absolute Values

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

### Compound Interest Questions

A) Suppose I want to have \$60,682.50 in my account for my children's college education. I expect to earn an average return of 12%, compounding four times a year. If I deposit \$25,000.00 today in my account, how many years will it take me to meet my goal (\$60,682.50 in my account)? b) Now suppose my goal is to have \$100,000.00

### Drawing a Venn Diagram

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.

### Venn Diagram for People Watching Football

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

### Finding the Greatest Common Divisor

Find the greatest common divisor of the following pairs: a)527, 765 (use technique like 527=341*1+186) b)361, 1178 (use technique like 527=341*1+186) c) -find the gcd (d) of 299, 481 (use technique like 31=186-155*1 --> 31=186-(341-186*1) -find integers such that 299x+481y=d -now replace 299 and 481 by 129 and 301.

### Binary Connections

Show that there are no complete single binary connectives other than NAND and NOR. Hint: Let f be the truth function for a complete binary connective. Show that f(true,true)=false and f(false,false)=true because the negation operation must be represented in terms of f. Then consider the remaining cases in the truth table for f