Insert ∈ or ∉ in each blank to make the resulting statement true. 13 _____ {3, 5, 12, 14}

Verified step by step guidance

1. Identify the set given in the problem: \( \{3, 5, 12, 14\} \).
2. Determine if the number 13 is an element of the set.
3. Check each element of the set to see if 13 matches any of them.
4. Since 13 is not found in the set, it is not an element of the set.
5. Therefore, the correct symbol to use is \( \notin \).

Key Concepts

Set Membership

Set membership refers to the relationship between an element and a set, indicating whether the element is part of the set. The symbol '∈' denotes that an element belongs to a set, while '∉' indicates that it does not. Understanding this concept is crucial for determining the correct relationship between the number 13 and the set {3, 5, 12, 14}.

Elements of a Set

In set theory, a set is a collection of distinct objects, known as elements. Each element can be a number, symbol, or even another set. To solve the question, one must identify whether 13 is included in the specified set, which consists of the numbers 3, 5, 12, and 14.

Logical Statements

Logical statements are assertions that can be evaluated as true or false. In this context, the statement formed by inserting '∈' or '∉' must accurately reflect the relationship between 13 and the set. Understanding how to construct and evaluate these statements is essential for arriving at the correct answer.