Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
1. Let \( A = \{1, 2, 3, 4, 5, 6\} \), and consider the following equivalence relation on \( A \): \( R = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (2,3), (3,2), (4,5), (5,4), (4,6), (6,4), (5,6), (6,5)\} \) List the equivalence classes of \( R \). 3. Let \( A = \{a, b, c, d, e\} \). Suppose \( R \) is an equivalence relation on \( A \). Suppose \( R \) has three equivalence classes. Also \( aRd \) and \( bRc \). Write out \( R \) as a set. 5. There are two different equivalence relations on the set \( A = \{a, b\} \). Describe them. Diagrams will suffice.
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Transcribed Image Text:1. Let \( A = \{1, 2, 3, 4, 5, 6\} \), and consider the following equivalence relation on \( A \): \( R = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (2,3), (3,2), (4,5), (5,4), (4,6), (6,4), (5,6), (6,5)\} \) List the equivalence classes of \( R \). 3. Let \( A = \{a, b, c, d, e\} \). Suppose \( R \) is an equivalence relation on \( A \). Suppose \( R \) has three equivalence classes. Also \( aRd \) and \( bRc \). Write out \( R \) as a set. 5. There are two different equivalence relations on the set \( A = \{a, b\} \). Describe them. Diagrams will suffice.
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