Let A₁ = {Su {i}: S = P({i+1, ..., 8, 9}) }. Prove that P ={A;:ie Z, 1 ≤ i ≤9} is a partition of P({1,..., 9})\{0}. Here P is the notation for power set.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 21E
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Let A₁ = {Su {i}: S = P({i+1, ..., 8, 9}) }. Prove that P = {A;:i €Z, 1 ≤ i ≤9} is a partition of P({1, ...,
9})\ {0}. Here P is the notation for power set.
Transcribed Image Text:Let A₁ = {Su {i}: S = P({i+1, ..., 8, 9}) }. Prove that P = {A;:i €Z, 1 ≤ i ≤9} is a partition of P({1, ..., 9})\ {0}. Here P is the notation for power set.
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