Consider the partial order with domain{3,5,6,7,10,14,20,30,60,70}and with x≤y if x evenly divides y. Select the correct Hasse diagram for the partial order
Consider the partial order with domain{3,5,6,7,10,14,20,30,60,70}and with x≤y if x evenly divides y. Select the correct Hasse diagram for the partial order
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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Consider the partial order with domain{3,5,6,7,10,14,20,30,60,70}and with x≤y if x evenly divides y. Select the correct Hasse diagram for the partial order

Transcribed Image Text:**Figure 2**: A Hasse diagram shows a set of elements 3; 5; 6; 7; 10; 14; 20; 30; 60; 70. The diagram illustrates the partial ordering of these elements. There are lines connecting 3 and 6, 6 and 30, 30 and 60, 5 and 10, 10 and 20, 20 and 60, 10 and 70, 7 and 14, 14 and 70.
### Detailed Explanation:
- **Elements:**
- The set comprises the numbers: 3, 5, 6, 7, 10, 14, 20, 30, 60, 70.
- **Lines Representing Relations:**
- **3 is connected to 6**
- **6 is connected to 30**
- **30 is connected to 60**
- **5 is connected to 10**
- **10 is connected to 20**
- **20 is connected to 60**
- **10 is connected to 70**
- **7 is connected to 14**
- **14 is connected to 70**
This Hasse diagram visually represents the hierarchical relationships and order between the elements based on divisibility or other criteria within the poset (partially ordered set). Each line indicates a direct connection without intermediaries, demonstrating the principles of transitivity and reduction in visualization.
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