Home
Back
Formula Used:
| From: | To: |
The complement of a set A, denoted as A', consists of all elements in the universal set U that are not in A. It represents the "opposite" or "remaining" elements when considering the universal set as the complete collection of all possible elements.
The calculator uses the formula:
Where:
Explanation: The formula simply subtracts the number of elements in set A from the total number of elements in the universal set to find how many elements are not in A.
Details: Calculating set complements is fundamental in set theory, probability, statistics, and various mathematical applications. It helps determine what elements are excluded from a particular set within a given context.
Tips: Enter the total number of elements in the universal set and the number of elements in set A. Ensure that the number of elements in set A does not exceed the number in the universal set.
Q1: What is a universal set?
A: A universal set is the set that contains all objects or elements under consideration for a particular discussion or problem.
Q2: Can the complement of a set be empty?
A: Yes, if set A contains all elements of the universal set, then its complement will be empty (n(A') = 0).
Q3: What is the relationship between a set and its complement?
A: A set and its complement are mutually exclusive (they have no elements in common) and together they make up the entire universal set.
Q4: Can the complement have more elements than the original set?
A: Yes, if the original set contains fewer than half of the elements in the universal set, its complement will have more elements.
Q5: How is set complement used in probability?
A: In probability theory, the complement rule states that P(A') = 1 - P(A), where A' is the complement of event A.