Determine whether each statement is true or false. 6 ∈ {2, 5, 8, 9}

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Understand the notation: The symbol $ \in $ means "is an element of" or "belongs to" a set.

Identify the set given: $ \{2, 5, 8, 9\} $ is a set containing the elements 2, 5, 8, and 9.

Check if the number 6 is listed as an element inside the set $ \{2, 5, 8, 9\} $.

Since 6 is not one of the elements 2, 5, 8, or 9, it does not belong to the set.

Therefore, the statement $ 6 \in \{2, 5, 8, 9\} $ is false.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Set Membership

Set membership refers to whether an element belongs to a given set. The symbol '∈' denotes 'is an element of,' so the statement '6 ∈ {2, 5, 8, 9}' asks if 6 is included in the set containing 2, 5, 8, and 9.

Set Notation

Set notation uses curly braces {} to list elements of a set explicitly. Understanding this notation helps identify which elements are included and is essential for evaluating membership statements.

True or False Statements in Mathematics

Determining the truth value of a statement involves verifying if the conditions hold. For membership, the statement is true if the element is in the set; otherwise, it is false.

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