6. Let R be the partial order which has the Hasse diagram shown. List the elements of R.
6. Let R be the partial order which has the Hasse diagram shown. List the elements of R.
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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6. Let \( R \) be the partial order which has the Hasse diagram shown. List the elements of \( R \).
**Description of the Hasse Diagram:**
- The diagram contains three elements: \( a \), \( b \), and \( c \).
- Element \( a \) is at the bottom of the diagram.
- Both \( b \) and \( c \) are directly above \( a \), indicating that \( a \) is related by the partial order to both \( b \) and \( c \) (i.e., \( a \leq b \) and \( a \leq c \)).
- There is an additional element \( d \) positioned above both \( b \) and \( c \), indicating that \( b \leq d \) and \( c \leq d \).
**Elements of \( R \):**
- The set \( R \) includes the elements \( a \), \( b \), \( c \), and \( d \) with the relations described by the Hasse diagram.
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