Union of two sets

Definition

The union of two sets is a set containing all unique elements from both sets. It is denoted by the symbol ∪.

5 Must Know Facts For Your Next Test

1. The union operation is commutative, meaning A ∪ B = B ∪ A.
2. The union of a set with the empty set results in the original set, i.e., A ∪ {} = A.
3. If an element is in either of the sets, it will be in their union.
4. The cardinality of the union can be found using |A ∪ B| = |A| + |B| - |A ∩ B|.
5. Visualizing unions using Venn diagrams helps to easily identify all elements included.

Review Questions

• What does the symbol ∪ represent?
• How do you find the cardinality of A ∪ B?
• Is it true that A ∪ {} = A for any set A?

Related terms

Intersection: The intersection of two sets is a set containing only the elements that are common to both sets, denoted by ∩.

Difference: The difference between two sets, denoted by A - B, is a set containing all elements that are in A but not in B.

Subset: A subset is a set where every element is also found within another set.