Question

Determine whether the given statement is true or false.

({2} in {2})

Answer 1

The given statement, "The element 2 is in the set {2}," is true.

Step-by-step explanation:

In set notation,
`\(\{2\}\)` represents a set containing the element 2. The statement
`\(({2} \text{ in } \{2\})\)` is true because it asserts that the element 2 is indeed an element of the set
`\(\{2\}\).` The notation "in" is used to denote set membership, indicating that 2 is a member of the set containing only the element 2. Therefore, the given statement is true.

Understanding set notation is essential in interpreting statements involving sets. In this case, the set
`\(\{2\}\)` contains the element 2, and the statement is evaluating whether 2 is a member of this set. The presence of 2 in the set
`\(\{2\}\)` confirms the truth of the statement.

In conclusion, the statement is true, as 2 is an element of the set
`\(\{2\}\)`. The notation
`\(({2} \text{ in } \{2\})\)` emphasizes the concept of set membership, providing a concise and accurate representation of the relationship between the element 2 and the set containing only that element.