15 on page 118 (parts a and b) Prove Theorem 2.30 Consider the rule for multiplication in Z, given by [a][b] = [ab] a.) Multiplication as defined by this rule is a binary operation on Z, b.) Multiplication is associative in Zn:

15 on page 118 (parts a and b) Prove Theorem 2.30 Consider the rule for multiplication in Z, given by [a][b] = [ab] a.) Multiplication as defined by this rule is a binary operation on Z, b.) Multiplication is associative in Zn:

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.1: Definition Of A Ring

Problem 11E: Assume R is a ring with unity e. Prove Theorem 5.8: If aR has a multiplicative inverse, the...

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.

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a.) Explain in your own words what the proof allows you to assume and requires you to show.

b.) Provide 2-3 examples to demonstrate the statement is true or false.

c.) Explain the meaning of any notation used in the problem and in your solution.

d.) Logically valid proof supported with justification.

15 on page 118 (parts a and b)
Prove Theorem 2.30
Consider the rule for multiplication in Z, given by
[a][b] = [ab]
a.) Multiplication as defined by this rule is a binary operation on Z,
b.) Multiplication is associative in Z:
[a]([b][c]) = ([a][b])[c]

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