Insert ∈ or ∉ in each blank to make the resulting statement true. {2} ____ {2, 4, 6, 8}

Verified step by step guidance

1. Understand the problem: We need to determine whether the element 2 is a member of the set {2, 4, 6, 8}. The symbol \( \in \) means 'is an element of,' and \( \notin \) means 'is not an element of.'
2. Look at the set given: {2, 4, 6, 8}. This set contains the numbers 2, 4, 6, and 8.
3. Check if the number 2 is listed inside the set. Since 2 is explicitly listed as the first element, it is indeed part of the set.
4. Therefore, the correct symbol to use between 2 and the set {2, 4, 6, 8} is \( \in \), indicating membership.
5. Write the complete true statement: \( 2 \in \{2, 4, 6, 8\} \).

Key Concepts

Set Membership (Element of) Symbol (∈)

The symbol ∈ denotes that an element belongs to a set. For example, if a number is contained within a set, we write that number ∈ the set. Understanding this symbol helps determine whether a specific element is included in a given set.

Set Non-membership Symbol (∉)

The symbol ∉ indicates that an element does not belong to a set. It is used to show that a particular item is not contained within the set. Recognizing when to use ∉ is essential for correctly expressing membership relations.

Set Notation and Elements

Sets are collections of distinct elements, often listed within curly braces {}. Understanding how to read and interpret sets, including identifying their elements, is fundamental to determining membership and applying the correct symbol (∈ or ∉).