Complement
All outcomes in the sample space that are not in an event
In mathematics, the complement of a set is all the elements of the universal set (a set that contains all possible elements) that are not in the set of interest.
For example, let’s say we have a universal set U = {1, 2, 3, 4, 5} and a set A = {2, 4}. The complement of set A, denoted as A’, would be all the elements of U that are not in set A. Therefore, A’ = {1, 3, 5}.
Another way to represent the complement of a set is by using a Venn diagram. The complement of set A would be all the elements outside of the circle that represents set A.
Complements are useful in many areas of mathematics, including set theory and probability. In set theory, the complement of a set can be used to find the intersection and union of sets. In probability, the complement of an event is used to find the probability of the event not happening.
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