Insert ∈ or ∉ in each blank to make the resulting statement true. 6 _____ {3, 4, 5, 6}

Verified step by step guidance

1. Identify the set given in the problem: $\{3,4,5,6\}$.
2. Determine if the number 6 is an element of the set.
3. Since 6 is listed in the set, it is an element of the set.
4. Use the symbol $\in$ to indicate that 6 is an element of the set.
5. The correct statement is: 6 $\in$ \{3, 4, 5, 6\}.

Key Concepts

Set Membership

Set membership refers to the relationship between an element and a set. An element 'a' is said to be a member of a set 'S' if 'a' is one of the objects contained in 'S'. This is denoted by the symbol '∈'. Conversely, if 'a' is not in 'S', it is denoted by '∉'. Understanding this concept is crucial for determining whether a specific number belongs to a given set.

Elements of a Set

In set theory, a set is a collection of distinct objects, considered as an object in its own right. The objects in a set are called elements. For example, in the set {3, 4, 5, 6}, the elements are 3, 4, 5, and 6. Recognizing the elements of a set helps in identifying whether a particular number is included in that set.

Notation in Set Theory

Set theory uses specific notation to convey relationships between elements and sets. The symbol '∈' indicates that an element is a member of a set, while '∉' indicates that it is not. Familiarity with this notation is essential for accurately interpreting and constructing statements about sets, such as determining the correct symbol to use in the given question.