Determine whether each statement is true or false. 6 ∈ {2, 5, 8, 9}

Verified step by step guidance

1. Understand the notation: The symbol \( \in \) means "is an element of" or "belongs to" a set.
2. Identify the set given: \( \{2, 5, 8, 9\} \) is a set containing the elements 2, 5, 8, and 9.
3. Check if the number 6 is listed as an element inside the set \( \{2, 5, 8, 9\} \).
4. Since 6 is not one of the elements 2, 5, 8, or 9, it does not belong to the set.
5. Therefore, the statement \( 6 \in \{2, 5, 8, 9\} \) is false.

Key Concepts

Set Membership

Set membership refers to whether an element belongs to a given set. The symbol '∈' denotes 'is an element of,' so the statement '6 ∈ {2, 5, 8, 9}' asks if 6 is included in the set containing 2, 5, 8, and 9.

Set Notation

Set notation uses curly braces {} to list elements of a set explicitly. Understanding this notation helps identify which elements are included and is essential for evaluating membership statements.

True or False Statements in Mathematics

Determining the truth value of a statement involves verifying if the conditions hold. For membership, the statement is true if the element is in the set; otherwise, it is false.