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Which of the following are one of the maximal and minimal elements respectively of the poset ({2, 4, 5, 10, 12, 20, 25}, /)
- a)25,5
- b)10, 4
- c)25, 4
- d)10, 5
Correct answer is option 'A'. Can you explain this answer?
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Which of the following are one of the maximal and minimal elements res...
Therefore, maximal elements are {12, 20, 25} and the minimal elements are {2, 5}.
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Which of the following are one of the maximal and minimal elements res...
To determine the maximal and minimal elements of a poset, we need to understand the definitions of these terms and apply them to the given poset.
Definition of Maximal Element:
A maximal element in a poset is an element that is not less than any other element in the poset. In other words, there is no element greater than the maximal element.
Definition of Minimal Element:
A minimal element in a poset is an element that is not greater than any other element in the poset. In other words, there is no element smaller than the minimal element.
Given poset: ({2, 4, 5, 10, 12, 20, 25}, /)
To find the maximal element, we need to check if there is any element that is not less than any other element.
- Maximal Element:
- We start by examining the elements in the poset one by one.
- 25 is the largest element in the poset. We check if there is any element greater than 25, but there isn't. Therefore, 25 is a maximal element.
To find the minimal element, we need to check if there is any element that is not greater than any other element.
- Minimal Element:
- We start by examining the elements in the poset one by one.
- 4 is the smallest element in the poset. We check if there is any element smaller than 4, but there isn't. Therefore, 4 is a minimal element.
Based on the above analysis, the correct answer is option 'A' (25, 5) as it correctly identifies 25 as the maximal element and 5 as the minimal element in the given poset.
Definition of Maximal Element:
A maximal element in a poset is an element that is not less than any other element in the poset. In other words, there is no element greater than the maximal element.
Definition of Minimal Element:
A minimal element in a poset is an element that is not greater than any other element in the poset. In other words, there is no element smaller than the minimal element.
Given poset: ({2, 4, 5, 10, 12, 20, 25}, /)
To find the maximal element, we need to check if there is any element that is not less than any other element.
- Maximal Element:
- We start by examining the elements in the poset one by one.
- 25 is the largest element in the poset. We check if there is any element greater than 25, but there isn't. Therefore, 25 is a maximal element.
To find the minimal element, we need to check if there is any element that is not greater than any other element.
- Minimal Element:
- We start by examining the elements in the poset one by one.
- 4 is the smallest element in the poset. We check if there is any element smaller than 4, but there isn't. Therefore, 4 is a minimal element.
Based on the above analysis, the correct answer is option 'A' (25, 5) as it correctly identifies 25 as the maximal element and 5 as the minimal element in the given poset.
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Which of the following are one of the maximal and minimal elements respectively of the poset ({2, 4, 5, 10, 12, 20, 25}, /)a)25,5b)10, 4c)25, 4d)10, 5Correct answer is option 'A'. Can you explain this answer?
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