In Exercises
See Figure

























Which condition fails to show that S is not a group with operation multiplication.
Given information:
The set
Explanation:
Let us check if the given table with operation multiplication is a group or not by using the definition given below:
Suppose the binary operation
1.
2.
3.
4.
Intermediate Algebra
Single Variable Calculus
Single Variable Calculus: Early Transcendentals, Volume I
Mathematical Applications for the Management, Life, and Social Sciences
Calculus: An Applied Approach (MindTap Course List)
Multivariable Calculus
Elementary Geometry For College Students, 7e
Mathematical Excursions (MindTap Course List)
Contemporary Mathematics for Business & Consumers
Applied Calculus
Elementary Technical Mathematics
Trigonometry (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Calculus: Early Transcendental Functions
Precalculus: Mathematics for Calculus (Standalone Book)
Finite Mathematics
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus (MindTap Course List)
Essentials Of Statistics
Finite Mathematics and Applied Calculus (MindTap Course List)
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Understanding Basic Statistics
Calculus: Early Transcendentals
Probability and Statistics for Engineering and the Sciences
Finite Mathematics for the Managerial, Life, and Social Sciences
Single Variable Calculus: Early Transcendentals
Calculus: Early Transcendental Functions (MindTap Course List)
Calculus of a Single Variable
Introduction To Statistics And Data Analysis
Study Guide for Stewart's Multivariable Calculus, 8th
Elementary Geometry for College Students
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
College Algebra (MindTap Course List)
Statistics for Business & Economics, Revised (MindTap Course List)
STATISTICS F/BUSINESS+ECONOMICSTEXT
Calculus (MindTap Course List)
Mathematics: A Practical Odyssey
Research Methods for the Behavioral Sciences (MindTap Course List)
Research Methods for the Behavioral Sciences (MindTap Course List)
Mathematics For Machine Technology