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5. Let R be a relation from the power set P(X) to itself, where X = {1,2,3, 4}, defined by A R B if A C B. a. Is A RA for all A E P(X)? Explain or give a counter-example. b. For any A, B E P(X), if A R B, is B R A? Explain or give a counter-example.

5. Let R be a relation from the power set P(X) to itself, where X = {1,2,3, 4}, defined by A R B if A C B. a. Is A RA for all A E P(X)? Explain or give a counter-example. b. For any A, B E P(X), if A R B, is B R A? Explain or give a counter-example.

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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Please help with question 5. Thank you.

**Problem 5:** Let \( R \) be a relation from the power set \( \mathcal{P}(X) \) to itself, where \( X = \{1, 2, 3, 4\} \), defined by \( A \, R \, B \) if \( A \subseteq B \). a. Is \( A \, R \, A \) for all \( A \in \mathcal{P}(X) \)? Explain or give a counter-example. b. For any \( A, B \in \mathcal{P}(X) \), if \( A \, R \, B \), is \( B \, R \, A \)? Explain or give a counter-example.
Transcribed Image Text:**Problem 5:** Let \( R \) be a relation from the power set \( \mathcal{P}(X) \) to itself, where \( X = \{1, 2, 3, 4\} \), defined by \( A \, R \, B \) if \( A \subseteq B \). a. Is \( A \, R \, A \) for all \( A \in \mathcal{P}(X) \)? Explain or give a counter-example. b. For any \( A, B \in \mathcal{P}(X) \), if \( A \, R \, B \), is \( B \, R \, A \)? Explain or give a counter-example.
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