Set Operations
One of the most important parts of set theory is understanding set operations. These allow us to form new sets from existing ones. The main operations are: union, intersection, difference, and complement.
Union
The union of two sets is the set of elements that appear in at least one of the sets. Notation: A ∪ B.
Intersection
The intersection of two sets is the set of elements that are found in both sets. Notation: A ∩ B.
Difference
The difference between two sets is the set of elements that are in the first set but not in the second. Notation: A − B.
Complement
The complement of a set relative to a universal set (U) is the set of elements in the universal set that are not in the examined set. Notation: A'.
Everyday Examples
- Union: the set of students in the class who play soccer or basketball.
- Intersection: the students who play both soccer AND basketball.
- Difference: the set of students who play soccer but not basketball.
- Complement: if U is all students, then A' is those who do not play soccer.
Practice Exercise
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