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Solution: Empty Sets | Sets and Functions - JEE PDF Download
1. The set has one member which 2. So, the given set is non empty.
2. Since there is no natural number between 1 and 2, the given set is an empty set.
3. Since no natural number can be simultaneously less than 5 and greater than 7, the given set is an empty set.
4. Since, 2 parallel lines can't have any point in common, the given set is an empty set.
Make yourself an honest man and then you may be sure there is one rascal less in the
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FAQs on Solution: Empty Sets - Sets and Functions - JEE
| 1. What is an empty set? |  |
Ans. An empty set, denoted by the symbol Ø or {}, is a set that does not contain any elements. It is a unique set as it is the only set that has no elements. In other words, it is a set with zero members.
| 2. How is an empty set represented in set theory? | |
Ans. In set theory, an empty set is represented by the symbol Ø or {}, which signifies that the set contains no elements. It is important to distinguish the empty set from a set that contains the element 0 or the number zero.
| 3. What are the properties of an empty set? | |
Ans. The empty set has some unique properties:
- The empty set is a subset of every set, including itself.
- The intersection of the empty set with any other set is always the empty set.
- The union of the empty set with any other set is equal to the other set.
| 4. How is the concept of an empty set used in mathematics? | |
Ans. The concept of an empty set is used in various branches of mathematics. It plays a crucial role in set theory, logic, and algebra. It helps in defining and understanding concepts such as subsets, intersections, and unions. The empty set also has applications in probability theory and combinatorics.
| 5. Can an empty set be considered as a null set? | |
Ans. Yes, the terms "empty set" and "null set" are often used interchangeably. Both terms refer to a set that does not contain any elements. The empty set is sometimes called a null set to emphasize its lack of elements.
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