Determine whether each statement is true or false. [6, 12, 14, 16} ∪ {6, 14, 19} = {6, 14}

Verified step by step guidance

1. Identify the operation: The symbol ∪ represents the union of two sets, which combines all the elements from both sets without repeating any elements.
2. List all unique elements from both sets: From the set {6, 12, 14, 16} and the set {6, 14, 19}, the unique elements are 6, 12, 14, 16, and 19.
3. Combine these elements into one set: The union of these sets will include every distinct element from both, which are 6, 12, 14, 16, and 19.
4. Compare the resulting set with the set {6, 14}: Check if the union set {6, 12, 14, 16, 19} is equal to {6, 14}.
5. Determine if the statement is true or false: Since the union set contains more elements than just 6 and 14, the statement is false.

Key Concepts

Set Union

Set union is an operation 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}.

Set Notation

Set notation is a mathematical language used to describe sets and their elements. Curly braces {} are used to denote a set, while elements are listed within these braces. Understanding how to read and interpret set notation is crucial for performing operations like union, intersection, and difference.

Element Membership

Element membership refers to whether a specific item is part of a set. This is denoted using the symbol ∈, meaning 'is an element of.' For instance, if we say 6 ∈ {6, 12, 14, 16}, it indicates that 6 is indeed an element of that set. This concept is essential for evaluating the truth of statements regarding sets.