Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∪ B.

Verified step by step guidance

1. Identify the elements in set A: $A=\{a,b,c\}$.
2. Identify the elements in set B: $B=\{a,c,d,e\}$.
3. The union of two sets, $A\cup B$, includes all elements that are in either set A or set B or in both.
4. List all unique elements from both sets A and B.
5. Combine the elements to form the union set $A\cup B$.

Key Concepts

Set Union

Set union is a fundamental operation in set theory that combines all unique elements from two or more sets. The union of sets A and B, denoted as A ∪ B, includes every element that is in A, in B, or in both. For example, if A = {1, 2} and B = {2, 3}, then A ∪ B = {1, 2, 3}.

Element Uniqueness

In set theory, each element in a set is unique, meaning that duplicates are not counted. When performing operations like union, any repeated elements from the involved sets are only included once in the resulting set. For instance, if A = {a, b} and B = {b, c}, then A ∪ B = {a, b, c}.

Set Notation

Set notation is a way to describe sets and their operations using specific symbols and terminology. Common symbols include curly braces for sets, the union symbol (∪) for combining sets, and the empty set symbol (∅) for a set with no elements. Understanding this notation is essential for accurately interpreting and performing set operations.