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Proposition. Suppose that A and B are sets. 1. Р(ANB) 3D Р(A)ПР(В). 2. P(A)UP(B)C P(AUB) with equality holding if and only if one of A or B is a subset of the other.

Proposition. Suppose that A and B are sets. 1. Р(ANB) 3D Р(A)ПР(В). 2. P(A)UP(B)C P(AUB) with equality holding if and only if one of A or B is a subset of the other.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Proposition on Sets and Power Sets** Form an argument that proves the following multi-part proposition addressing a distributive-type property of the power set constructor with the union and intersection of sets. **Proposition.** Suppose that A and B are sets. 1. **P(A ∩ B) = P(A) ∩ P(B).** 2. **P(A) ∪ P(B) ⊆ P(A ∪ B)** with equality holding if and only if one of A or B is a subset of the other.
Transcribed Image Text:**Proposition on Sets and Power Sets** Form an argument that proves the following multi-part proposition addressing a distributive-type property of the power set constructor with the union and intersection of sets. **Proposition.** Suppose that A and B are sets. 1. **P(A ∩ B) = P(A) ∩ P(B).** 2. **P(A) ∪ P(B) ⊆ P(A ∪ B)** with equality holding if and only if one of A or B is a subset of the other.
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