Insert ∈ or ∉ in each blank to make the resulting statement true. 0 _____ {0, 5, 6, 7, 8, 10}

Verified step by step guidance

1. Identify the meaning of the symbols: ∈ means 'is an element of' and ∉ means 'is not an element of'.
2. Examine the set given: \( \{0, 5, 6, 7, 8, 10\} \).
3. Determine if the number 0 is listed within the set.
4. Since 0 is present in the set, the correct symbol to use is ∈.
5. Insert the symbol: 0 ∈ \{0, 5, 6, 7, 8, 10\}.

Key Concepts

Set Notation

Set notation is a mathematical language used to describe collections of objects, known as elements. In this context, the set {0, 5, 6, 7, 8, 10} contains specific numbers, and understanding how to interpret this notation is crucial for determining whether an element belongs to the set.

Element Membership

Element membership refers to the relationship between an element and a set, denoted by the symbols ∈ (is an element of) and ∉ (is not an element of). To solve the question, one must assess whether the number 0 is included in the given set, which directly influences the choice of symbol.

Logical Statements

Logical statements are assertions that can be evaluated as true or false. In this case, the statement formed by inserting either ∈ or ∉ must accurately reflect the relationship between the number 0 and the set. Understanding how to construct and evaluate these statements is essential for arriving at the correct answer.