Mathematics Exam > Mathematics Questions > The set S = [0, 1] hasa)maximal element onlyb...
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The set S = [0, 1] has
- a)maximal element only
- b)minimal element only
- c)Both maximal and minimal element
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The set S = [0, 1] hasa)maximal element onlyb)minimal element onlyc)Bo...
Question Analysis:
The question asks us to determine the elements of the set S = [0, 1] that can be classified as maximal, minimal, or both. We need to understand the definitions of maximal and minimal elements to answer this question correctly.
Definitions:
- A maximal element in a set is an element that is greater than or equal to all other elements in the set.
- A minimal element in a set is an element that is less than or equal to all other elements in the set.
Answer Explanation:
To determine the maximal and minimal elements in the set S = [0, 1], we need to compare each element to all other elements in the set.
Minimal Element:
- The element 0 is the smallest element in the set S = [0, 1].
- It is less than or equal to all other elements in the set, as 0 <=>
- Therefore, 0 is a minimal element of the set S.
Maximal Element:
- The element 1 is the largest element in the set S = [0, 1].
- It is greater than or equal to all other elements in the set, as 1 >= 0.
- Therefore, 1 is a maximal element of the set S.
Conclusion:
The set S = [0, 1] has both a minimal element (0) and a maximal element (1). Therefore, the correct answer is option 'C' - Both maximal and minimal element.
The question asks us to determine the elements of the set S = [0, 1] that can be classified as maximal, minimal, or both. We need to understand the definitions of maximal and minimal elements to answer this question correctly.
Definitions:
- A maximal element in a set is an element that is greater than or equal to all other elements in the set.
- A minimal element in a set is an element that is less than or equal to all other elements in the set.
Answer Explanation:
To determine the maximal and minimal elements in the set S = [0, 1], we need to compare each element to all other elements in the set.
Minimal Element:
- The element 0 is the smallest element in the set S = [0, 1].
- It is less than or equal to all other elements in the set, as 0 <=>
- Therefore, 0 is a minimal element of the set S.
Maximal Element:
- The element 1 is the largest element in the set S = [0, 1].
- It is greater than or equal to all other elements in the set, as 1 >= 0.
- Therefore, 1 is a maximal element of the set S.
Conclusion:
The set S = [0, 1] has both a minimal element (0) and a maximal element (1). Therefore, the correct answer is option 'C' - Both maximal and minimal element.
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Community Answer
The set S = [0, 1] hasa)maximal element onlyb)minimal element onlyc)Bo...
Because this contains its supremum and infimum both,so when a set contains its supremum then it is called its maximal element,same for infimum
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The set S = [0, 1] hasa)maximal element onlyb)minimal element onlyc)Both maximal and minimal elementd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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