Insert ∈ or ∉ in each blank to make the resulting statement true. 6 _____ {3, 4, 5, 6}

Verified step by step guidance

1. Understand the problem: We need to determine whether the number 6 is an element of the set {3, 4, 5, 6}.
2. Recall the meaning of the symbols: The symbol \( \in \) means "is an element of," and \( \notin \) means "is not an element of."
3. Look at the set \( \{3, 4, 5, 6\} \) and check if the number 6 is listed inside the curly braces.
4. Since 6 appears in the set, the correct symbol to use is \( \in \), indicating membership.
5. Write the complete true statement: \( 6 \in \{3, 4, 5, 6\} \).

Key Concepts

Set Membership (Element of a Set)

Set membership refers to whether a specific element belongs to a given set. The symbol '∈' denotes that an element is a member of the set, meaning it is included within the set's listed elements.

Set Notation and Symbols

Set notation uses curly braces {} to list elements, and symbols like '∈' and '∉' to indicate membership or non-membership. Understanding these symbols is essential to correctly interpret and complete statements about sets.

Evaluating Membership Statements

To determine if an element belongs to a set, compare the element with the set's listed members. If the element matches any member, use '∈'; if not, use '∉'. This evaluation is fundamental in set theory problems.