Recognizing Set Operations — Let A = {1,2,3}, B = {3,4}. Select the correct statements!

The union is {1,2,3,4}, the intersection {3}, A - B {1,2}. However, B - A is {4}, not {2,4}.

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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