Reference no: EM131027668
For a mapping %:A -> B, let == denote the kernel equivalence of %, and let *:A -> A== denote the natural mapping. Define $:A== -> B by $([a]) = %(a) for every equivalence class [a] in A==.
1. Show that $ is well defined and one-to-one, and that $ is onto if % is onto. Furthermore, show that % = $*, so that % is the composite of an onto mapping followed by a one-to-one mapping.
2. If %(A) is a finite set, show that the set A== of equivalence classes is also finite and that the cardinality of A== is equal to the cardinality of %(A) (called the Bijection Theorem).
3. In each of the following two cases, find the cardinality of A== for the given set A and the given mapping %:
i. A = U X U, where U = {1, 2, 3, 4, 6, 12}, and %:A -> Q is defined by %(n, m) = n/m, where Q is the set of all rational numbers.
ii. A = {n: n is an element of Z and 1 <= n <= 99}, where Z is the set of all integers, and %:A -> N is defined by %(n) = the sum of the digits of n, where N is the set of all natural numbers.
The operations definition emphasizes decision
: The Operations definition emphasizes decision, function and process elements of the organization. Briefly discuss the need to address these fundamental elements.
|
How much money has lose-a-digit budgeted for the year
: The amount of the budget just happens to be the smallest number of cents (other than one cent) that is a perfect square, a perfect cube, and a perfect fifth power." How much money has Lose-a-digit budgeted for the year?
|
Compute the book depreciation expense
: Collins used the stamping machine for 2,450 hours to produce 23,450 units. From the information given, compute the book depreciation expense for 2016 under each of the following methods.
|
How was the universal declaration of human rights similar
: How was the Universal Declaration of Human Rights (1948) similar to the Declaration of the Rights of the Russian People (1917), the French Declaration of the Rights of Man (1789).
|
Find the cardinality of a== for the given set a
: If %(A) is a finite set, show that the set A== of equivalence classes is also finite and that the cardinality of A== is equal to the cardinality of %(A) (called the Bijection Theorem).
|
Situations surrounding the ethical dilemma
: Write a 700- to 1,050-word paper. Reflect on an ethical dilemma that you have faced in your career, or a recent accounting scandal in the news. Describe the situations surrounding the ethical dilemma and your actions in response.
|
Discuss from where various innovation types emanate
: From a general perspective, explain and discuss from where various innovation types emanate in organizations and identify the types of innovations that various organizational sources produce.
|
Project - production of an automobile
: Introduce the language of manufacturing by providing an integrated coverage of manufacturing processes and manufacturing systems - Project topic will be the Production of an automobile.
|
Prepare a presentation for a group
: "Assume you are a senior partner in an accounting firm and must prepare a presentation for a group of recruits who aspire to become auditors with your firm. Prepare a 10- to 12-slide presentation that includes detailed speaker notes discussing eac..
|