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

Verified step by step guidance

1. Understand the symbol \( \in \), which means 'is an element of'.
2. Identify the set given in the problem: \( \{2, 5, 6, 8\} \).
3. Check if the number 3 is listed as one of the elements in the set.
4. Since 3 is not listed among the elements \( \{2, 5, 6, 8\} \), determine the truth value of the statement.
5. Conclude whether the statement '3 \( \in \) \{2, 5, 6, 8\}' is true or false based on your findings.

Key Concepts

Set Notation

Set notation is a mathematical way to describe a collection of distinct objects, known as elements. In this context, the notation {2, 5, 6, 8} represents a set containing the numbers 2, 5, 6, and 8. Understanding set notation is crucial for determining membership, which indicates whether a specific element belongs to a given set.

Element Membership

Element membership refers to the relationship between an element and a set, denoted by the symbol '∈'. If an element is part of a set, we say it is a member of that set. For example, in the statement 3 ∈ {2, 5, 6, 8}, we need to assess whether the number 3 is included in the specified set to determine the truth value of the statement.

True or False Statements

True or false statements are logical assertions that can be evaluated as either true or false. In mathematics, determining the truth value of a statement often involves checking conditions or relationships, such as membership in a set. Understanding how to evaluate these statements is essential for logical reasoning and problem-solving in algebra.