Union and Intersection of Sets
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In set theory, union and intersection are two fundamental operations that can be performed on sets.
Union of Sets:
The union of two sets A and B, denoted by A ∪ B, is the set of all elements that belong to either A or B or both. In other words, if x belongs to A or x belongs to B, then x belongs to A ∪ B.
Example: Let A = {1, 2, 3} and B = {3, 4, 5}. The union of A and B, denoted by A ∪ B, is {1, 2, 3, 4, 5}.
Intersection of Sets:
The intersection of two sets A and B, denoted by A ∩ B, is the set of all elements that belong to both A and B. In other words, if x belongs to A and x belongs to B, then x belongs to A ∩ B.
Example: Let A = {1, 2, 3} and B = {3, 4, 5}. The intersection of A and B, denoted by A ∩ B, is {3}.
It is important to note that if A and B are disjoint sets (i.e., they have no common elements), then their intersection is empty (i.e., A ∩ B = ∅). Similarly, if A is a subset of B (i.e., every element of A also belongs to B), then their intersection is equal to A (i.e., A ∩ B = A).
In conclusion, the union and intersection of sets are important operations in set theory that allow us to manipulate and analyze sets in a variety of contexts.
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