Determine whether each statement is true or false. {1, 2, 4} ∪ {1, 2, 4} = {1, 2, 4}

Verified step by step guidance

1. Recall the definition of the union of two sets: The union of sets A and B, 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: Both sets are \(\{1, 2, 4\}\) and \(\{1, 2, 4\}\).
3. Apply the union operation: Since both sets are identical, their union will include all elements from either set, which are \(1\), \(2\), and \(4\).
4. Write the union explicitly: \(\{1, 2, 4\} \cup \{1, 2, 4\} = \{1, 2, 4\}\).
5. Conclude whether the statement is true or false based on the union result matching the given set.

Key Concepts

Set Union

The union of two sets combines all unique elements from both sets into one set. If an element appears in either set, it is included in the union. For example, the union of {1, 2} and {2, 3} is {1, 2, 3}.

Set Equality

Two sets are equal if they contain exactly the same elements, regardless of order or repetition. For instance, {1, 2, 3} equals {3, 2, 1} because they have identical members.

Idempotent Law of Union

The idempotent law states that the union of a set with itself is the set itself. Formally, A ∪ A = A. This means combining a set with itself does not add new elements.