Find {16, 18, 21, 50} ∪ {15, 16, 17, 18}.

Verified step by step guidance

1. Understand that the union of two sets, denoted by \(A \cup B\), is the set containing all elements that are in \(A\), or in \(B\), or in both.
2. Identify the two sets given: \(A = \{16, 18, 21, 50\}\) and \(B = \{15, 16, 17, 18\}\).
3. List all elements from set \(A\): \$16, 18, 21, 50$.
4. Add all elements from set \(B\) that are not already in set \(A\): \$15, 17\( (since \)16\( and \)18$ are already included).
5. Combine all unique elements to form the union: \(\{15, 16, 17, 18, 21, 50\}\).

Key Concepts

Set Theory

Set theory studies collections of distinct objects, called sets. It provides the foundation for understanding operations like union, intersection, and difference between sets, which are essential for solving problems involving groups of elements.

Union of Sets

The union of two sets combines all unique elements from both sets into one set. It is denoted by the symbol ∪ and includes every element that appears in either or both sets, without duplication.

Element Uniqueness in Sets

In sets, each element is unique and appears only once, regardless of how many times it is listed. When performing operations like union, repeated elements are counted only once to maintain the set's property of distinctness.