Intersection of two sets

Definition

The intersection of two sets is a new set containing all the elements that are common to both original sets. The symbol for intersection is ∩.

5 Must Know Facts For Your Next Test

1. If A and B are two sets, their intersection is denoted as A ∩ B.
2. The intersection of any set with the empty set is always the empty set.
3. For finite sets, the number of elements in A ∩ B can be found using |A ∩ B| = |A| + |B| - |A ∪ B|.
4. Intersection is commutative, meaning A ∩ B = B ∩ A.
5. The intersection of two sets can be visualized using a Venn diagram where the overlapping region represents A ∩ B.

Review Questions

• What symbol is used to denote the intersection of two sets?
• How do you find the intersection of two finite sets using their cardinalities?
• Is the operation of finding the intersection of two sets commutative?

Related terms

Union: The union of two sets is a new set containing all elements that belong to either one or both of the original sets.

Difference: The difference between two sets, A and B (denoted as A - B), contains elements that are in A but not in B.

Complement: The complement of a set includes all elements not in the specified set, typically within a universal set context.