Let A = {1, 2, 3, 4, 5}. Define a relation on the power set P(A) by declaring that (X, Y ) ∈ R if and only if the sets X and Y have the same number of elements.(a) Prove that R is an equivalence relation.(b) Find the equivalence classes [{2}]. (X,Y) E R if and only if the sets X and Y have the same number of elements.(a) Prove that R is an equivalence relation.(b) Find the equivalence classes [{2}]. Let A{1,2, 3, 4, 5}. Define a relation on the power set P(A) by declaring that

Let A be a non empty set, A relation R on A is said to be an equivalent relation if 1) R is…

Let A = {1, 2, 3, 4, 5}. Define a relation on the power set P(A) by declaring that (X, Y ) ∈ R if and only if the sets X and Y have the same number of elements. (a) Prove that R is an equivalence relation. (b) Find the equivalence classes [{2}].

Let A = {1, 2, 3, 4, 5}. Define a relation on the power set P(A) by declaring that (X, Y ) ∈ R if and only if the sets X and Y have the same number of elements. (a) Prove that R is an equivalence relation. (b) Find the equivalence classes [{2}].

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...

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Question

Let A = {1, 2, 3, 4, 5}. Define a relation on the power set P(A) by declaring that (X, Y ) ∈ R if and only if the sets X and Y have the same number of elements.

(a) Prove that R is an equivalence relation.

(b) Find the equivalence classes [{2}].