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 **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.

The domain is 3, 5, 6, 7, 10, 14, 20, 30, 60, 70. The partial order on the above domain is defined…

Answered: Consider the partial order with…

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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Question

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

**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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