Explain how to use set notation.

Set notation is a way to describe collections of objects, typically numbers, using curly brackets and specific symbols.

In set notation, a set is usually denoted by a capital letter, such as \( A \) or \( B \). The elements or members of the set are listed within curly brackets \(\{ \}\). For example, the set of even numbers between 1 and 10 can be written as \( \{2, 4, 6, 8, 10\} \).

There are different ways to describe sets. One common method is the **roster method**, where all elements are listed explicitly. For instance, \( A = \{1, 3, 5\} \) means set \( A \) contains the numbers 1, 3, and 5.

Another method is the **set-builder notation**, which describes the properties that the elements of the set must satisfy. For example, \( B = \{ x \mid x \text{ is an even number between 1 and 10} \} \) means set \( B \) includes all \( x \) such that \( x \) is an even number between 1 and 10.

Special symbols are often used in set notation. The symbol \( \in \) means "is an element of," so \( 3 \in A \) means 3 is an element of set \( A \). Conversely, \( \notin \) means "is not an element of," so \( 4 \notin A \) means 4 is not an element of set \( A \).

Sets can also be described using intervals. For example, the set of all real numbers between 1 and 5, including 1 but not 5, is written as \( [1, 5) \).

Understanding set notation is essential for describing and analysing groups of numbers or objects in mathematics.