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Set Operations - 2 Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
FAQs on Set Operations - 2 Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What are set operations in mathematics? |  |
Ans. Set operations in mathematics refer to the various actions or manipulations that can be performed on sets, such as union, intersection, and complement. These operations help to combine, compare, or modify sets based on defined rules.
| 2. What is the union of two sets? | |
Ans. The union of two sets is an operation that combines all the elements from both sets, without duplication. It is denoted by the symbol "∪". For example, if set A = {1, 2, 3} and set B = {3, 4, 5}, then the union of A and B is A∪B = {1, 2, 3, 4, 5}.
| 3. How is the intersection of two sets calculated? | |
Ans. The intersection of two sets is an operation that identifies the common elements between the sets. It is denoted by the symbol "∩". To find the intersection, we compare the elements of both sets and include only those elements that are present in both sets. For example, if set A = {1, 2, 3} and set B = {3, 4, 5}, then the intersection of A and B is A∩B = {3}.
| 4. What is the complement of a set? | |
Ans. The complement of a set, also known as the relative complement or set difference, refers to the elements that belong to one set but not the other. It is denoted by the symbol "−" or "\". For example, if set A = {1, 2, 3} and set B = {3, 4, 5}, then the complement of A with respect to B is B\A = {4, 5}.
| 5. Can sets have an empty intersection? | |
Ans. Yes, sets can have an empty intersection. If two sets do not share any common elements, their intersection will be an empty set, denoted by the symbol "∅". This occurs when there are no elements that are present in both sets.
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