3. Let A be a set with A = 4. Let C be relation defined on pow(A), the powerset of A, as follows: For all sets X, Y E pow(A), XC Yiff |X = Y. Determine if C is reflexive, symmetric, transitive, or none of these. Is C an equivalence relation? If yes, how many equivalence classes are there for C?

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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3. Let A be a set with A = 4. Let C be relation defined on pow(A), the powerset of A, as follows:
For all sets X, Y E pow(A), XC Yiff |X = Y. Determine if C is reflexive, symmetric, transitive, or
none of these. Is C an equivalence relation? If yes, how many equivalence classes are there for C?
Transcribed Image Text:3. Let A be a set with A = 4. Let C be relation defined on pow(A), the powerset of A, as follows: For all sets X, Y E pow(A), XC Yiff |X = Y. Determine if C is reflexive, symmetric, transitive, or none of these. Is C an equivalence relation? If yes, how many equivalence classes are there for C?
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