2. Verify and show whether each of the following is a groupoid, semigroup, monoid, or N/A in case that the mathematical structure is neither a groupoid, semigroup nor monoid. (2 points cach) (a) (Z". +), where in Z" denotes the set of all non-positive integers. (b) (N, +), where denotes the usual division. (c) (Zen,), where denotes the usual multiplication.
2. Verify and show whether each of the following is a groupoid, semigroup, monoid, or N/A in case that the mathematical structure is neither a groupoid, semigroup nor monoid. (2 points cach) (a) (Z". +), where in Z" denotes the set of all non-positive integers. (b) (N, +), where denotes the usual division. (c) (Zen,), where denotes the usual multiplication.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![2. Verify and show whether each of the following is a groupoid, semigroup, monoid,
or N/A in case that the mathematical strueture is neither a groupoid, semigroup
nor monoid. (2 points each)
(a) (Z", +), where in Z" denotes the set of all non-positive integers.
(b) (N, +), where denotes the usual division.
(c) (Z, -), where denotes the usual multiplication.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa32f51be-e159-4130-ad1a-234f17f65164%2F47f9fad2-c652-43f1-8566-d7921186075f%2Fiag3wgw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Verify and show whether each of the following is a groupoid, semigroup, monoid,
or N/A in case that the mathematical strueture is neither a groupoid, semigroup
nor monoid. (2 points each)
(a) (Z", +), where in Z" denotes the set of all non-positive integers.
(b) (N, +), where denotes the usual division.
(c) (Z, -), where denotes the usual multiplication.
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