To say that a set A is tidy means that, for every x, if x is an element of A, then is a subset of A. Also recall that, for any set X, we have defined the successor ofX, S(X), to be the set XU{X}. 1. Suppose that U and V are both tidy. Prove that U n V is tidy. 2. Suppose that X is tidy. Prove that S(X) is tidy.
To say that a set A is tidy means that, for every x, if x is an element of A, then is a subset of A. Also recall that, for any set X, we have defined the successor ofX, S(X), to be the set XU{X}. 1. Suppose that U and V are both tidy. Prove that U n V is tidy. 2. Suppose that X is tidy. Prove that S(X) is tidy.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 9E: 9. The definition of an even integer was stated in Section 1.2. Prove or disprove that the set of...
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To say that a set A is tidy means that, for every x, if x is an element of A, then x is a subset of A. Also recall that, for any set X, we have defined the successor of X, S ( X ), to be the set X ∪ { X }.
- Suppose that U and V are both tidy. Prove that U ∩ V is tidy.
- Suppose that X is tidy. Prove that S ( X ) is tidy.
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