complement
In mathematics, the term “complement” refers to the set of elements that are not included in a given set
In mathematics, the term “complement” refers to the set of elements that are not included in a given set. More specifically, the complement of a set A, denoted as A’, is the set of all elements that are in the universal set but not in A.
To better understand this concept, let’s consider an example. Suppose we have a universal set U that consists of all even numbers less than 10: U = {2, 4, 6, 8}. If we define a set A as A = {2, 6}, then the complement of set A, denoted as A’, would be {4, 8}, which includes all the elements from the universal set U that are not in set A.
To find the complement of a set, we typically subtract the elements of the set from the universal set. In our example, A’ = U – A. This means that we remove the elements of A from the universal set U to obtain the complement A’.
It’s important to note that the complement of a set can vary depending on the universal set being considered. For example, if we change the universal set U in our example to include all even numbers less than 20, then the complement A’ would be different.
Complements are often used in set theory and probability to represent the elements that are not part of a certain set. They can help in solving various mathematical problems and understanding the relationships between sets.
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