Set of sets Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
FAQs on Set of sets Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is a set in mathematics? |  |
Ans. In mathematics, a set is a collection of distinct objects, considered as an entity itself. It is a well-defined collection of elements or members, which can be anything like numbers, letters, or even other sets.
| 2. How are sets represented? | |
Ans. Sets can be represented in different ways. The most common method is by listing the elements within curly braces, separating them with commas. For example, a set of even numbers can be represented as {2, 4, 6, 8, ...}. Another method is by using set-builder notation, where a condition is given to describe the elements of the set. For instance, {x | x is a positive integer} represents the set of all positive integers.
| 3. What is the cardinality of a set? | |
Ans. The cardinality of a set refers to the number of elements it contains. It is denoted by the symbol 'n' or by writing '|' before the set name. For example, if A = {1, 2, 3}, then the cardinality of set A is 3, which can be written as n(A) = 3 or |A| = 3.
| 4. What is the difference between a subset and a proper subset? | |
Ans. A subset is a set where all the elements of one set are also present in another set. In other words, if every element of set A is also an element of set B, then A is a subset of B. On the other hand, a proper subset is a subset where all the elements of one set are present in another set, but the second set contains additional elements that are not in the first set.
| 5. How are sets related to mathematical operations? | |
Ans. Sets are closely related to mathematical operations such as union, intersection, and complement. The union of two sets A and B is a set that contains all the elements present in either A or B. The intersection of two sets A and B is a set that contains only the elements common to both A and B. The complement of a set A with respect to a universal set U is a set that contains all the elements in U but not in A. These operations allow us to perform various calculations and comparisons involving sets.
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