Let A be a nonempty set and let P be a partition of A. Define a relation R (corresponding to P) on A by x Ry if there exists S e P such that x, y E S. (*) (a) Let A = {1, 2, 3}. Write down ALL possible partitions of A. For each of the partition P. use (*) to write down the relation R (as a subset of A x A) corresponding to P.

Let A be a nonempty set and let P be a partition of A. Define a relation R (corresponding to P) on A by x Ry if there exists S e P such that x, y E S. () (a) Let A = {1, 2, 3}. Write down ALL possible partitions of A. For each of the partition P. use () to write down the relation R (as a subset of A x A) corresponding to P.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...

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