Determine whether each statement is true or false. 9 ∉ {8, 5, 2, 1}

Key Concepts

Set Notation

Set notation is a mathematical way to describe a collection of distinct objects, known as elements. In this context, the notation {8, 5, 2, 1} represents a set containing the numbers 8, 5, 2, and 1. Understanding set notation is crucial for determining whether a specific element, such as 9, belongs to the set.

Element Membership

Element membership refers to the relationship between an element and a set, denoted by the symbol '∈' for 'is an element of' and '∉' for 'is not an element of.' In the question, the statement '9 ∉ {8, 5, 2, 1}' asserts that 9 is not one of the elements in the specified set. Recognizing this relationship is essential for evaluating the truth of the statement.

True or False Statements

True or false statements are assertions that can be evaluated as either correct or incorrect. In mathematical logic, determining the truth value of a statement involves analyzing its components and their relationships. In this case, the statement about the membership of 9 in the set must be assessed to conclude whether it is true or false.