Let
” defined on
a. Prove that “congruence modulo
” is an equivalence relation.
b. List five members of each of the equivalence classes
a)
To prove:
The relation “congruence modulo
Formula Used:
The relation “congruence modulo n” is defined on the set Z of all integers as follows:
x is congruent to y modulo n if and only if
Proof:
A relation R on a nonempty set A is an equivalence relation if the following conditions are satisfied for arbitrary x, y, and z in A:
1.
2. If
3. If
Consider the relation
1.
2.
b)
Five members of each of the following equivalence classes
Intermediate Algebra
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Contemporary Mathematics for Business & Consumers
Elementary Technical Mathematics
Applied Calculus
Calculus (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendentals
Probability and Statistics for Engineering and the Sciences
Mathematical Excursions (MindTap Course List)
Essentials Of Statistics
Understanding Basic Statistics
Statistics for The Behavioral Sciences (MindTap Course List)
Calculus: Early Transcendental Functions
Calculus: An Applied Approach (MindTap Course List)
Trigonometry (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Mathematical Applications for the Management, Life, and Social Sciences
Finite Mathematics
Elementary Geometry For College Students, 7e
Multivariable Calculus
Single Variable Calculus
Calculus of a Single Variable
Calculus: Early Transcendental Functions (MindTap Course List)
Finite Mathematics for the Managerial, Life, and Social Sciences
Single Variable Calculus: Early Transcendentals
Elementary Geometry for College Students
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Introduction To Statistics And Data Analysis
College Algebra (MindTap Course List)
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Statistics for Business & Economics, Revised (MindTap Course List)
Multivariable Calculus
Calculus (MindTap Course List)
Mathematics For Machine Technology
Research Methods for the Behavioral Sciences (MindTap Course List)
Research Methods for the Behavioral Sciences (MindTap Course List)