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Discrete Math

Vector Space Proof

1. a) Let A be a set equipped with a (closed) binary operation * . If x is an arbitrary element of A, is x*x*x always an associative product? Explain. Justify your answer. b) Prove or disprove part a. Be complete and thorough in proof writing.

Solve: The Inductive Hypothesis

Let P (n) be the statement that 1^3 + 2^3 + â?¦ +n^3=(n(n+1)/2)^2 for the positive integer n. a. What is the statement P(1)? b. Show that P(1) is true, completing the basis step of that proof. c. What is the inductive hypothesis? d. What do you need to prove in the inductive step? e. Complete the inductive step. f. Exp

A survey of flower gardeners

A survey of flower gardeners showed the following: 87 grew roses 15 grew both roses and tulips 8 grew all three types 27 grew tulips 11 grew both orchids and tulips 7 grew none of these three 26 grew orchids 19 grew both roses and orchids Create a Venn diagram to reflect the above data, label your

Analyses of Euclidean Algorithms

a) When we write a=mb+r in the Euclidean algorithm, call the number m a multiplier. How do the multipliers influence how long it takes the Euclidean algorithm to run? b) For which multipliers will the Euclidean algorithm take as long as possible to run? c) For two steps, three steps, and four steps, find the smallest pai

Application of a Venn Diagram

A charity asked people attending a fundraiser cookout if they ate the salad, casserole or dessert. Here is the Venn diagram of the results. Of those surveyed, how many people ate casserole, but not dessert? (Points : 3)

Proof for if x and y are odd then xy is odd

Hello, I was hoping someone could help me with this homework problem? I have looked through my text and notes and I cannot figure this out. The problem is below. Thank you, in advance, for your help!! Prove the following: If x is any odd integer and y is any odd integer then xy is an odd integer.

Bit String and Rule of Products

A bit string is a string of bits (0â??s and 1â??s). The length of a bit string is the number of bits in the string. An example, of a bit string of length four is 0010. An example, of a bit string of length five is 11010. Use the Rule of Products to determine the following: (a) How many bit strings are there of length eig

Find the value of x.

What is the value of x after each of the following statements are encountered in a computer program, if x = 1 before the statement is reached. Explain fully. (a) if 2 + 2 = 5 AND 3 + 4 = 7 then x:= x + 1 (b) if 2 + 3 = 5 XOR 3 + 4 = 8 then x:= x + 1

Venn Diagram Probabilities /Permutations.

Consider the Venn Diagram attached in Word document below. The numbers in the regions of the circle indicate the number of items that belong to that region. Determine: 1. n(A) 2. n(B) 3. P(A) 4. P(B) 5. P(A/B) 6. P(B/A)

Probability is demonstrated.

PRACTICE PROBLEMS: 1. Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). A. rolling a sum of 11 on two fair six sided dice B. drawing a red ni

Explore statistics/probability

1. Light Switches A working light bulb is in a closed room with no windows. Outside the room, is a panel of three switches, one of which controls the light inside (up is on, down is off.) You may do anything you like to the three switches and then enter the room to inspect the light. After this, without any further experiment

Financial Management

Solve for the unknown number of years in each of the following (Round your answers to 2 decimal places. (e.g., 32.16)): Present Value Years Interest Rate Future Value $700 ? 10% $1,997 890 ? 6 3,400 17,400

Venn diagram is constructed.

1. List all the subsets of { 8, 16, 27, 31} 2. Determine the number of subsets of {mom, dad, son, daughter} 3. At MegaSalad, a salad can be ordered with some, all, or none of the following set of ingredients on top of the salad greens: {ham, turkey, chicken, tomato, feta cheese, cheddar cheese, cucumbers, onions, red pep

Cyclic groups

Describe what cyclic groups are and show that they are abelian. Describe their structure and the structure of their subgroups and factor groups up to isomorphism.

Determine Truth Value for Propositions using Symbolic Logic

1) Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement 17 ≥ 17 and −3 > −2 2) Write the statement in symbolic form. Let p: The tent is pitched. q: The bonfire is burning. The tent is pitched and the bonfire is burning 3) D

upstream or downstream transfers

Justings Co. owned 80% of Evana Corp. During 2006, Justings sold to Evana land with a book value of $48,000. The selling price was $70,000. A. Create the eliminations regarding this transaction for 2006 and 2007, TL and *TL.

Plotting Data and Calculations using Venn Diagrams

A survey of fruit tree growers showed the following: 71 grew raspberries 25 grew both raspberries and blueberries 46 grew blueberries 16 grew both raspberries and strawberries 31 grew strawberries 20 grew both blueberries and strawberries 11 grew all three ty

Binary variables

The Decision Sciences department head at a university will be scheduling faculty to teach courses during the coming fall semester. Three required courses need to be scheduled. The three courses are at the UG, MBA, and MS levels. Three professors will be assigned to the courses, with each professor receiving one of the courses. S

Set Theory Problems

Create two sets, set A and set B. Set A will be a list of five items you personally NEED to buy the most (essential items). Set B will be a list of five items that you WANT to buy the most (fun stuff). List the items in Set A and Set B, and also list or state the items in the union and in the intersection of Set A an

State Standards and DAP

Optain the academic standards for kindergarten for three states (available on state education websites). Compare the standards in a single category such as math or reading and describe how the standards are similar or different across the states. What are your thoughts regarding the developmental appropriates of these standards?

Facts about the Cantor Set

A) Prove that the Cantor set C is nowhere dense in E (contains no interval of E). b) Prove that every point of C is a limit point of C; that is for very a in C and every epsilon > 0, there is b in C with |a-b| < epsilon. A closed set with this property is said to be perfect.

Discrete Math

What is the value of x after each of the following statements are encountered in a computer program, if x = 1 before the statement is reached. Explain fully. (a) if 2 + 3 = 6 AND 3 + 4 = 7 then x:= x + 1 (b) if 2 + 3 = 6 XOR 3 + 4 = 7 then x:= x + 1

Find roots.

Note the cubic equation x3 - 6x2 + 11x - 6 = 0. I will claim that x = 1 constitutes a root of that equation ( replace x by 1 in the equation to verify ). Thus, the binomial (x - 1) will divide our cubic equation evenly, without remainder. Perform the division to obtain the quotient, which is a quadratic equation. Completely