Insert ∈ or ∉ in each blank to make the resulting statement true. 5 ____ {4, 6, 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: \{4, 6, 8, 10\}.
3. Determine if the number 5 is listed in the set \{4, 6, 8, 10\}.
4. Since 5 is not listed in the set, it is not an element of the set.
5. Therefore, insert the symbol ∉ in the blank to make the statement true: 5 ∉ \{4, 6, 8, 10\}.

Key Concepts

Set Notation

Set notation is a mathematical way to describe a collection of distinct objects, known as elements. In this context, the set {4, 6, 8, 10} contains the numbers 4, 6, 8, and 10. Understanding how to interpret and manipulate sets is crucial for determining whether a specific element belongs to a set.

Element of a Set

The notation '∈' indicates that an element is a member of a set, while '∉' indicates that it is not a member. For example, if we say '5 ∈ {4, 6, 8, 10}', it means that 5 is one of the elements in the set. Conversely, '5 ∉ {4, 6, 8, 10}' means that 5 is not included in the set, which is the case here.

Logical Statements

Logical statements are assertions that can be evaluated as true or false. In this question, the task is to determine the truth value of the statement regarding the membership of the number 5 in the given set. Understanding how to construct and evaluate these statements is essential for solving problems involving set theory.