Posets And Hasse Diagrams

Step 1: Understanding the Hasse diagram.
In a Hasse diagram, the least upper bound (LUB) is the smallest element that is greater than or equal to all elements in the set, and the greatest lower bound (GLB) is the largest element that is less than or equal to all elements in the set.

Step 2: Identify the least upper bound.
The least upper bound of the set $%5C%7BX%2C%20Y%2C%20Z%5C%7D$ is the smallest element that is greater than or equal to both $X$ , $Y$ , and $Z$ . Based on the diagram, the least upper bound is $T$ .

Step 3: Identify the greatest lower bound.
The greatest lower bound of the set $%5C%7BX%2C%20Y%2C%20Z%5C%7D$ is the largest element that is less than or equal to both $X$ , $Y$ , and $Z$ . From the diagram, the greatest lower bound is $Y$ .

Step 4: Conclusion.
Thus, the correct answer is (4) The least upper bound is $T$ and the greatest lower bound is $Y$ .

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Posets And Hasse Diagrams

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs