Question: Let I be if Niel Ai a nonempty set. A family of sets {Aifier is mutually and is pairwise disjoint if for all i

Let I be if Niel Ai a nonempty set. A family of

Let I be if Niel Ai a nonempty set. A family of sets {Aifier is mutually and is pairwise disjoint if for all i j in I, we have j in I, we have disjoint An A, A, n A, a) Give an example of a family of sets (Ailier that is neither pairwise disjoint nor pairwise intersecting. b) Suppose that I contains more than one element. Show: if {A}ier is pair- wise disjoint, then it is mutually disjoint. c) Find a family of sets A1, A2, A3 that is mutually disjoint but not pairwise disjoint. . A family is pairwise intersecting if for all i .

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

The Crazy Eddie fraud may appear smaller and gentler than the massive billion-dollar frauds exposed in recent times, such as Bernie Madoffs Ponzi scheme, frauds in the subprime mortgage market, the...

KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

Using superposition, find the deflection of the steel shaft at A in the figure. Find the deflection at midspan. By what percentage do these two values differ? Take the magnitude of force (F) to be...

Cesar's Bottlers bottles soft drinks in a factory that can operate one shift, two shifts, or three shifts per day. Each shift is eight hours long. The factory is closed on weekends. The sales price...

Let R be any ring (possibly without identity) and Fa free R-module on the set X, with L : X F, as in Exercise 2. Show that L (X) is a set of generators of the R-module F. is commutative. Conclude...

Let R be a ring with identity. Show that R is not a free module on any set in the category of all R-modules (as defined in Exercise 2). Data from in exercise 2 Let R be any ring (possibly without...

Let R be any ring (possibly without identity) and X a nonempty set. In this exercise an R-module Fis called a free module on X if F is a free object on X in the category of a/I left R-modules. Thus...

1 Due September 6 Problems 1.20, 1.26, 1.30 from the textbook Add-on sketch of a proof of existence of a set which is not Lebesgue-measurable. The original example is due to G. Vitali. Let = [0, 1);...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Hess' Principle Use the following information to calculate the heat of formation of propane, C3Hg. 3 C (graph) + 4 H (g) C3Hg (g) 1. C (graph) + O (g) CO (g) DH = - 393.5 kJ 2. 1. H(g) + O2(g) HO...

Examine the aging schedule that CAE provides in Note 5. How does the aging schedule help you assess the company's credit management? What's the importance of separating the amount into different...

Select all that apply Social capital can help buld trusting relationships that can provide which of the following career benefits? faster advancement reased threlaneod to chinge careers higher status...

Which of the following grouped frequency distribution is constructed correctly? A. Class Frequen 1 -5 18 6 - 10 13 11 - 15 21 - 11 25 26 - 30 Cla Freque ncy 1-5 18 6 - 13 10 11 - 15 3, B.

11. Kate is a researcher biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, the temperature at the time of application, and water treatment after application. She has 4...

C. Determinant of Matrix 1 - 2 1 2-i - i sin x -1 csc x -2 sin x| 1 C = 1 - 5 1 B = 1-i 2i cos x 3i 12 A = 1 1 -1 2 3 1 1+2i 3i 1 tanx cot x 1 2i 1 - sin x 2 1 4 2 1 3 1. Cofactor Expansion 2....

Create a class named BloodData that includes fields that hold a blood type (the four blood types are O , A , B , and AB ) and a Rh factor (the factors are + and ). Create a default constructor that...

You are now required to develop a Contingency Plan , using Appendix A , for each area where something could go wrong and how you will recover demonstrating understanding of risks. Appendix A BOUNCE...

If f(x)=|x+1|+3 and g(x)=2^(x), find all values of x, to the nearest tenth, for which f(x)=g(x)

Use induction to show that a nonempty binary tree with n nodes has height at least lg n.

Add the attribute n to each proto-vEB structure, giving the number of elements currently in the set it represents, and write pseudocode for PROTO-VEB-DELETE that uses the attribute n to decide when...

a. The incidence matrix for an undirected graph G D (V, E) is a |V| |E| matrix M such that M e = 1 if edge e is incident on vertex , and M e = 0 otherwise. Argue that a set of columns of M is...

1. What trade- offs are involved in each of these decisions? a. Deciding whether to use two- sigma or three- sigma control limits. b. Choosing between a large sample size and a smaller sample size....

Analysis of the output of a process has suggested that the variability is nonrandom on several occasions recently. However, each time an investigation has not revealed any assignable causes. What are...

Suppose you are going to have a prescription filled at a local pharmacy. Referring to the dimensions of service quality for each dimension, give an example of how you would judge the quality of the...