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The figure below shows an arrow diagram for a partial order: 8 What are the maximal elements in the partial order? О 1,3, 5, 8 О 1,3, 5 O 7,8 O 1, 2, 3, 5, 8

The figure below shows an arrow diagram for a partial order: 8 What are the maximal elements in the partial order? О 1,3, 5, 8 О 1,3, 5 O 7,8 O 1, 2, 3, 5, 8

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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The image depicts an arrow diagram representing a partial order. This diagram consists of nodes labeled from 1 to 8, with arrows indicating relationships between these nodes. ### Explanation of the Arrow Diagram: - **Nodes 1** has a loop and arrows pointing to nodes 2 and 3. - **Node 2** has a loop and no other arrows. - **Node 3** has a loop and arrows pointing to nodes 1, 5, and 6. - **Node 4** has a loop and arrows pointing to nodes 3, 6, and 7. - **Node 5** has a loop and arrows pointing to nodes 3, 6, and 7. - **Node 6** has a loop and arrows pointing to nodes 5, 4, 3, 1, and 2. - **Node 7** has a loop and arrows pointing to nodes 5 and 6. - **Node 8** has a loop and no other arrows. ### Question: What are the maximal elements in the partial order? ### Multiple Choice Options: - ○ 1, 3, 5, 8 - ○ 1, 3, 5 - ○ 7, 8 - ○ 1, 2, 3, 5, 8 **Note:** Maximal elements in a partial order are those nodes that are not less than any other node with respect to the partial order relationship.
Transcribed Image Text:The image depicts an arrow diagram representing a partial order. This diagram consists of nodes labeled from 1 to 8, with arrows indicating relationships between these nodes. ### Explanation of the Arrow Diagram: - **Nodes 1** has a loop and arrows pointing to nodes 2 and 3. - **Node 2** has a loop and no other arrows. - **Node 3** has a loop and arrows pointing to nodes 1, 5, and 6. - **Node 4** has a loop and arrows pointing to nodes 3, 6, and 7. - **Node 5** has a loop and arrows pointing to nodes 3, 6, and 7. - **Node 6** has a loop and arrows pointing to nodes 5, 4, 3, 1, and 2. - **Node 7** has a loop and arrows pointing to nodes 5 and 6. - **Node 8** has a loop and no other arrows. ### Question: What are the maximal elements in the partial order? ### Multiple Choice Options: - ○ 1, 3, 5, 8 - ○ 1, 3, 5 - ○ 7, 8 - ○ 1, 2, 3, 5, 8 **Note:** Maximal elements in a partial order are those nodes that are not less than any other node with respect to the partial order relationship.
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