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Set Theory - Miscellaneous, Quantitative Reasoning Video Lecture | Quantitative for GMAT
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FAQs on Set Theory - Miscellaneous, Quantitative Reasoning Video Lecture - Quantitative for GMAT
| 1. What is set theory? |  |
Ans. Set theory is a branch of mathematical logic that deals with the study of collections of objects, called sets. It provides a foundation for understanding mathematical structures by defining concepts such as union, intersection, subset, and complement of sets.
| 2. How is set theory applied in mathematics? | |
Ans. Set theory is used as a fundamental tool in various branches of mathematics, such as algebra, analysis, and topology. It provides a framework for defining mathematical objects and operations, allowing mathematicians to rigorously study concepts like numbers, functions, and geometric shapes.
| 3. What are the basic operations in set theory? | |
Ans. The basic operations in set theory are union, intersection, and complement. The union of two sets A and B is the set containing all elements that are in either A or B. The intersection of sets A and B is the set of elements that are common to both A and B. The complement of a set A is the set of all elements that are not in A.
| 4. How do you determine if one set is a subset of another? | |
Ans. To determine if one set is a subset of another, we compare the elements of the two sets. A set A is considered a subset of another set B if every element in A is also an element of B. In other words, if every element of A is contained within B, then A is a subset of B.
| 5. What is the cardinality of a set? | |
Ans. The cardinality of a set is a measure of the "size" or number of elements in the set. It is denoted by the symbol |A|, where A is the set. For finite sets, the cardinality is simply the count of elements in the set. For example, if a set A has 5 elements, its cardinality is |A| = 5. For infinite sets, the cardinality can be more complex and is described using different sizes of infinity, such as countably infinite or uncountably infinite.
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Nov 21, 2024 Last updated |
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