Let A be the set of points different from the origin in the Euclidean plane. For
Prove that ~ defines an equivalence relation on A.
Find the equivalence classes of ~.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Additional Math Textbook Solutions
Mathematics for the Trades: A Guided Approach (10th Edition) - Standalone book
Finite Mathematics (11th Edition)
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
Introductory Combinatorics
Mathematical Ideas (13th Edition) - Standalone book
- Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.arrow_forwardLabel each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.arrow_forwardLabel each of the following statements as either true or false. Every mapping on a nonempty set A is a relation.arrow_forward
- 23. Let be the equivalence relation on defined by if and only if there exists an element in such that .If , find , the equivalence class containing.arrow_forwardLet (A) be the power set of the nonempty set A, and let C denote a fixed subset of A. Define R on (A) by xRy if and only if xC=yC. Prove that R is an equivalence relation on (A).arrow_forwardLet be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,