91Ó°ÊÓ

When studying sets, an important idea is understanding what it means for something to be an 'element of a set'. A set is a collection of distinct objects, called elements. These elements can be anything: numbers, letters, or even other sets. The symbol used to denote 'membership' is \( \in \). For instance, if you see \( 3 \in \{1, 2, 3, 4\} \), it means that 3 is an element of the set \( \{1, 2, 3, 4\} \).

Conversely, if an element is not in a set, you use the symbol \( otin \). So, if you see \( 5 otin \{1, 2, 3, 4\} \), it means that 5 is not an element of the set \( \{1, 2, 3, 4\} \).

To verify if an element belongs to a set:

• Identify the set in question.
• List out all the elements of the set.
• Check if the element is among those listed.

Understanding set notation is crucial when working with sets. Sets are usually denoted by curly braces \( \{ \} \). Inside these braces, the elements of the set are listed, separated by commas. For example, \( \{a, b, c\} \) represents a set with elements 'a', 'b', and 'c'. These elements can be numbers, letters, or even objects.

When using set notation:

• Always use curly braces \( \{ \} \) to define a set.
• Separate each element with a comma.

For example, in the exercise, the set notation \( \{2, 4, 6, 9, 17\} \) tells us that the set contains the numbers 2, 4, 6, 9, and 17.

We then use the membership symbol \( \in \) to ask if a particular element is within this set. The statement \( 7 \in \{2, 4, 6, 9, 17\} \) asks whether 7 is an element of the set that contains 2, 4, 6, 9, and 17.

In mathematics, we often use 'true' or 'false' statements to verify the validity of a given condition. When someone presents a statement about set membership, you will determine whether it is true or false by examining the elements of the set.

Let's look at our exercise again:

• The given set is \( \{2, 4, 6, 9, 17\} \).
• The statement to verify is whether \( 7 \in \{2, 4, 6, 9, 17\} \).

To check if this statement is true:

• List out the elements: 2, 4, 6, 9, and 17.
• See if 7 is among these elements.

Since 7 is not in the list, the statement \( 7 \in \{2, 4, 6, 9, 17\} \) is false. Therefore, the correct response to the exercise is that the statement is false.

In summary, checking if statements about set memberships are true or false is a systematic process involving:

• Identifying the set.
• Listing out the elements.
• Determining whether the stated element is in the set.