Determine whether each statement is true or false. 1 ∈ {11, 5, 4, 3, 1}

Verified step by step guidance

1. Understand the problem: We need to determine if the number 1 is an element of the set \{11, 5, 4, 3, 1\}.
2. Recall the definition of set membership: An element \(a\) is in a set \(S\) if \(a\) is listed as one of the elements of \(S\). This is denoted as \(a \in S\).
3. Look at the given set \(\{11, 5, 4, 3, 1\}\) and check if the number 1 appears among the elements listed.
4. Since 1 is explicitly listed as an element of the set, it means \(1 \in \{11, 5, 4, 3, 1\}\) is true.
5. Therefore, the statement \(1 \in \{11, 5, 4, 3, 1\}\) is true.

Key Concepts

Set Membership

Set membership refers to whether an element belongs to a given set. If an element is listed within the curly braces defining the set, it is considered a member. For example, 1 ∈ {11, 5, 4, 3, 1} means checking if 1 is an element of that set.

Notation for Sets

Sets are typically denoted by curly braces {} containing distinct elements separated by commas. The symbol '∈' means 'is an element of,' and is used to express membership. Understanding this notation is essential for interpreting and answering questions about sets.

True or False Statements in Mathematics

Determining whether a statement is true or false involves verifying the claim based on definitions or properties. In this case, the statement '1 ∈ {11, 5, 4, 3, 1}' is true if 1 is found in the set, otherwise false. This skill is fundamental in logic and proofs.