Let~ be the equivalence relation on Z defined by ~y if and only if z Give three examples of elements in the equivalence class of -2. Example # 1: Example #2: Example #3: Consider the relation R on the set {1, 2, 3} defined by Is R an equivalence relation? OA. Yes OB. No y is divisible by 15. {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. because... (select all that apply) A. R is reflexive, symmetric, and transitive. B. R is not reflexive. C. R is not symmetric. D. R is not transitive. E. None of the above

Let~ be the equivalence relation on Z defined by ~y if and only if z Give three examples of elements in the equivalence class of -2. Example # 1: Example #2: Example #3: Consider the relation R on the set {1, 2, 3} defined by Is R an equivalence relation? OA. Yes OB. No y is divisible by 15. {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. because... (select all that apply) A. R is reflexive, symmetric, and transitive. B. R is not reflexive. C. R is not symmetric. D. R is not transitive. E. None of the above

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 3E: a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the...

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Question

Discrete math: please solve both questions correctly

Let be the equivalence relation on Z defined by ay if and only if z-y is divisible by 15.
Give three examples of elements in the equivalence class of -2.
Example #1:
Example # 2:
Example #3:
Consider the relation R on the set {1, 2, 3} defined by
Is R an equivalence relation?
O A. Yes
OB. No
{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}.
because... (select all that apply)
A. R is reflexive, symmetric, and transitive.
B. R is not reflexive.
C. R is not symmetric.
D. R is not transitive.
E. None of the above

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