Determine whether each statement is true or false. 3 ∈ {2, 5, 6, 8}

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: \( \{2, 5, 6, 8\} \) is a set containing the elements 2, 5, 6, and 8.
3. Check if the number 3 is listed as an element inside the set \( \{2, 5, 6, 8\} \).
4. Since 3 is not one of the elements in the set, it does not belong to the set.
5. Therefore, the statement \( 3 \in \{2, 5, 6, 8\} \) 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 '3 ∈ {2, 5, 6, 8}' asks if 3 is included in the set containing 2, 5, 6, and 8.

Set Notation

Set notation uses curly braces {} to list elements of a set explicitly. Understanding how to read and interpret these braces is essential to identify which elements are contained within the set.

True or False Statements in Mathematics

Determining the truth value of a statement involves verifying if the conditions stated are met. In this case, checking if the element is in the set confirms whether the statement is true or false.