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Which of the following sets is an empty set?
- a){x : x is a natural number less than 1}
- b){1, 2, 3}
- c){0}
- d){a, b, c, d}
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Which of the following sets is an empty set?a) {x : x is a natural num...
Understanding the Empty Set
The concept of an empty set is fundamental in mathematics, especially in set theory. An empty set contains no elements at all, often denoted by the symbol ∅ or represented by {}.
Analyzing the Options
Let's examine each option to identify which one represents an empty set:
Conclusion
Among the options provided, only option A is the empty set, as it contains no natural numbers less than 1. The other options contain one or more elements, making them non-empty sets. Understanding the empty set is crucial, as it lays the foundation for more complex mathematical concepts.
The concept of an empty set is fundamental in mathematics, especially in set theory. An empty set contains no elements at all, often denoted by the symbol ∅ or represented by {}.
Analyzing the Options
Let's examine each option to identify which one represents an empty set:
- a) {x : x is a natural number less than 1}
- Natural numbers start from 1 (i.e., 1, 2, 3, ...).
- There are no natural numbers less than 1.
- Therefore, this set is empty: ∅. - b) {1, 2, 3}
- This set contains the elements 1, 2, and 3.
- It is not empty. - c) {0}
- This set contains one element, which is 0.
- It is also not empty. - d) {a, b, c, d}
- This set contains four elements: a, b, c, and d.
- It is not empty either.
Conclusion
Among the options provided, only option A is the empty set, as it contains no natural numbers less than 1. The other options contain one or more elements, making them non-empty sets. Understanding the empty set is crucial, as it lays the foundation for more complex mathematical concepts.
Community Answer
Which of the following sets is an empty set?a) {x : x is a natural num...
The set {x : x is a natural number less than 1} has no elements, thus it is an empty set, often denoted by Ø.
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