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The half interval [0, l) have
- a)maximal element only
- b)minimal element only
- c)maximal and minimal both element
- d)no maximal and no minimal element.
Correct answer is option 'B'. Can you explain this answer?
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The half interval [0, l) havea)maximal element onlyb)minimal element o...
The Half Interval [0, l)
The given half interval [0, l) represents the set of real numbers starting from 0 and going up to but not including l. In this interval, we need to determine if there is a maximal element, a minimal element, both, or neither.
Definitions:
Before we proceed with the analysis, let's first define the terms "maximal element" and "minimal element" for a set.
- A maximal element is an element in a set that is greater than or equal to all other elements in that set.
- A minimal element is an element in a set that is less than or equal to all other elements in that set.
Analysis:
To determine if there is a maximal or minimal element in the half interval [0, l), we need to consider the properties of this interval.
- The interval starts from 0, so 0 is a potential minimal element as it is less than or equal to all other elements in the interval.
- However, there is no upper bound specified for the interval. It only goes up to, but does not include, l. Therefore, there is no element in the interval that is greater than or equal to all other elements. This means that there is no maximal element in the interval.
Conclusion:
Based on the analysis, we can conclude that the half interval [0, l) has a minimal element but no maximal element.
Answer: The correct answer is option 'B' (minimal element only).
The given half interval [0, l) represents the set of real numbers starting from 0 and going up to but not including l. In this interval, we need to determine if there is a maximal element, a minimal element, both, or neither.
Definitions:
Before we proceed with the analysis, let's first define the terms "maximal element" and "minimal element" for a set.
- A maximal element is an element in a set that is greater than or equal to all other elements in that set.
- A minimal element is an element in a set that is less than or equal to all other elements in that set.
Analysis:
To determine if there is a maximal or minimal element in the half interval [0, l), we need to consider the properties of this interval.
- The interval starts from 0, so 0 is a potential minimal element as it is less than or equal to all other elements in the interval.
- However, there is no upper bound specified for the interval. It only goes up to, but does not include, l. Therefore, there is no element in the interval that is greater than or equal to all other elements. This means that there is no maximal element in the interval.
Conclusion:
Based on the analysis, we can conclude that the half interval [0, l) has a minimal element but no maximal element.
Answer: The correct answer is option 'B' (minimal element only).
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Community Answer
The half interval [0, l) havea)maximal element onlyb)minimal element o...
Since supremum of [0,1) is 1 but 1 doesn't belong to [0,1), so there is no maximal element, but the infimum is 0 which belong to [0,1) so, there is only minimal element is 0.
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The half interval [0, l) havea)maximal element onlyb)minimal element onlyc)maximal and minimal both elementd)no maximal and no minimal element.Correct answer is option 'B'. Can you explain this answer?
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