Determine whether each statement is true or false. {3, 5, 9, 10} ∪ ∅ = {3, 5, 9, 10}

Key Concepts

Set Union

Set union is an operation that combines all unique elements from two or more sets. When performing a union, if an element appears in any of the sets, it will be included in the resulting set. For example, the union of {1, 2} and {2, 3} is {1, 2, 3}.

Empty Set

The empty set, denoted as ∅, is a set that contains no elements. It is a fundamental concept in set theory, serving as the identity element for the union operation. When any set is united with the empty set, the result is the original set itself.

Set Equality

Two sets are considered equal if they contain exactly the same elements, regardless of the order or repetition of those elements. For instance, {1, 2, 3} is equal to {3, 2, 1}. Understanding set equality is crucial for determining the truth of statements involving sets.