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

Verified step by step guidance

1. Identify the elements of the set \( \{0, 1, 2, 5\} \).
2. Determine if the element \( 0 \) is present in the set \( \{0, 1, 2, 5\} \).
3. Since \( 0 \) is listed as an element in the set, it belongs to the set.
4. Use the symbol \( \in \) to indicate that \( 0 \) is an element of the set.
5. The correct statement is \( \{0\} \in \{0, 1, 2, 5\} \).

Key Concepts

Set Notation

Set notation is a mathematical language used to describe collections of objects, known as sets. In this context, the set {0, 1, 2, 5} contains the elements 0, 1, 2, and 5. Understanding how to read and interpret set notation is crucial for determining relationships between elements and sets.

Element of a Set (∈)

The symbol '∈' denotes that an element is a member of a set. For example, if we say '0 ∈ {0, 1, 2, 5}', it means that 0 is included in the set. Recognizing when an element belongs to a set is essential for correctly filling in the blanks in the given statement.

Not an Element of a Set (∉)

The symbol '∉' indicates that an element is not a member of a set. For instance, '3 ∉ {0, 1, 2, 5}' means that 3 is not part of the set. Understanding this concept helps in determining the correct relationship between the element and the set in the question.