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Functions, Enumeration Schemes and Bijection

Let f:Z+ --> Z be the function defined by... f(n) = {n/2 n even { -(n-1)/2 n odd ? n even; The following table indicates the enumeration scheme behind the definiton of the function. n .......... 7 5 312468... f(n)..... ?3 ?2 ?1 0 1 2 3 4... Show that f is a bijection. [You may assume basic facts about the

Max and min

(See attached file for full problem description) --- First: solve this problem. Second: check my answer. Third: if my answer is wrong or incomplete explain why. Find the absolute max and min of on [-8,8] My answer: On the interval [-8,8], f has an absolute max at f(0) = 0 and an absolute min at f(-8) = -14

Binomial Coefficients and Combinations

Four people select a main dish from a menu of 7 items. How many choices are possible: a) If a record is kept of who selected which choice (as a waiter would) b) If who selected which choice is ignored (as a chef would). Analyze this part by the number of different choices made.

Lebesgue Measurable Set

Let A be a set in R^n, we denote by A + x_o a parallel shift of A by x_o to A + x_o, A + x_o = { x : x = y + x_o, y in A}. Now, if A is a lebesgue measurable then show that 1). x_o + A is also lebesgue measurable 2). m(A) = m(x_o + A) Can someone check my answer and tell me if it is correct or not? My work: s

Lebesgue Measurable Sets, Compact Sets and Open Sets

If A is lebesgue measurable sets in R^n, bounded, then there is a compact set K_epsilon and an open set for every epsilon > 0 V_epsilon such that K_epsilon is subset of A and A is a subset of V_epsilon and for m(A-K) < epsilon m(V-K) < epsilon

Decision-Making Mathematics : Arranging Combinations of Sports Leagues Fixtures

In addition to each tem playing every other team in the league once at home and once away, the matches should be arranged such that: (1) each team only has one match per week (2) for any team no two matches should be successively at home or away (3) for any team no two successive matches should be against the same opposing

Power set and bijection

I have two small problems. I need all the work shown and in the second problem please answer in detail and NOT just yes or no. (See attached file for full problem description)

Combination Application Word Problems and Summations

Exercise # 1 A) How many nonnegative integer solutions are there to the pair of equations: And B) How many ways are there to distribute 20 toys to m children such that the first two children get the same number of toys if: 1- The toys are identical? 2- The toys are distinct? Exercise #2

Combinations Application Word Problem

A person has 3 different letters to write, 2 interviews to do, and 2 commercials to review. In making aschedule, (first, second, etc.) how many different combinations are there?


A disk jockey can play 7 songs during his program. If there are 13 songs to chose from, in how many different orders can the song be arranged?


How many four letter codes can be formed using A,B,C,D,E and F? No letter can be used more than once.

Random walk

Hi I would appreciate if you could help me with this question. Is the question below TRUE or FALSE and explain why ? Question: I have two random walks, both starting at 0 and with a reflecting boundary at 0. Each Step, Walk A goes up 1 with probability 1/2 and down 1 with probability 1/2(except at the boundary). Each

Sequences : Measurable Subsets and Cantor Sets (2 Problems)

1) a. Let with . If is a measurable subset of R, prove that and are measurable. b. let E =[0,1]Q. Prove that E is measurable and (E)=1. c. let P denote the cantor set in [0,1]. Prove that 2) If E R, prove that ther exists a sequence { } of open sets with E for all n such that = . -

Counting techniques

I am having a hard time trying to understand an example problem in my math book. The problem goes: In how many ways can 3 white tiles, 2 blue tiles, and 2 red tiles be arranged in a single row?( I also need to assume that the tiles are identical except for color.)

Sets, Counting and Grouping

Out of 30 job applicants, 11 are female, 17 are college graduates, 7 are bilingual, 3 are female college graduates, 2 are bilingual woman, 6 are bilingual college graduates, and 2 are bilingual female college graduates. What is the number of women who are not college graduates but nevertheless are bilingual?

How different statistical devices can be used in business?

How the following statistical devices can be used in business today? Describe their usefulness and how businessman can be benefit, or how to help them in making sound decisions. (Explain individually) --probability --probability distributions --normal distribution --permutation and combinations