Insert ∈ or ∉ in each blank to make the resulting statement true. {0} _____ {0, 1, 2, 5}

Verified step by step guidance

1. Understand the problem: We need to determine whether the element 0 is a member of the set {0, 1, 2, 5} or not. The symbol \( \in \) means "is an element of," and \( \notin \) means "is not an element of."
2. Recall the definition of set membership: An element \( a \) is in a set \( S \) if \( a \) is one of the elements listed in \( S \).
3. Look at the set \( \{0, 1, 2, 5\} \) and check if 0 is listed as one of its elements.
4. Since 0 is indeed listed in the set, the correct symbol to use is \( \in \), meaning 0 is an element of the set.
5. Write the complete true statement: \( 0 \in \{0, 1, 2, 5\} \).

Key Concepts

Set Membership (Element of) Symbol (∈)

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

Set Notation and Elements

Sets are collections of distinct objects, often listed within curly braces {}. Recognizing the elements of a set is essential to verify membership. For instance, {0, 1, 2, 5} contains the elements 0, 1, 2, and 5.

Negation of Membership Symbol (∉)

The symbol ∉ indicates that an element does not belong to a set. If an element is not found in the set, we write a ∉ A. This concept is crucial to correctly complete statements about set membership.