union (A U B)
a set consisting of all of the elements that are in sets A and B (no repeating)
In set theory, the union of two sets A and B is defined as the set that contains all the elements that belong to either A or B or both of them. It is denoted by A U B.
Mathematically,
A U B = {x : (x belongs to A) or (x belongs to B)}
For example, consider two sets A and B as:
A = {1, 2, 3, 4}
B = {2, 4, 6, 8}
The union of sets A and B, denoted by A U B, will be:
A U B = {1, 2, 3, 4, 6, 8}
As we can see, all the elements from both the sets A and B are included in the union set, without any repetition.
It is important to note that the union of sets is commutative, i.e., A U B = B U A, and associative, i.e., (A U B) U C = A U (B U C).
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