We are looking at sets written out in two different formats. Match the name of the format to each of the following sets. {TE A |x is even} set builder notation {dog, cat, fish, bearkat} [roster notation { animal: the animal makes a good pet } [set builder notation {4, 6, 8, 24, 78} roster notation

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**Understanding Set Notations: An Educational Guide**

In this section, we will explore sets written in two different formats and correctly identify the notation used for each example. This understanding is fundamental in set theory, helping to distinguish between methods of representing sets.

1. **Example 1:**
   - **Set:** \(\{ x \in A \mid x \text{ is even} \}\)
   - **Format:** Set Builder Notation
     - **Explanation:** This set describes all elements \( x \) in a certain set \( A \) where \( x \) is an even number. It uses a condition to define the set.

2. **Example 2:**
   - **Set:** \(\{ \text{dog, cat, fish, bearcat} \}\)
   - **Format:** Roster Notation
     - **Explanation:** This set lists its elements directly. The elements are specific animals, and the set is defined by explicitly enumerating its members.

3. **Example 3:**
   - **Set:** \(\{ \text{animal: the animal makes a good pet} \}\)
   - **Format:** Set Builder Notation
     - **Explanation:** This set uses a descriptive condition to include elements. Any animal that makes a good pet is part of the set, defined by the given property.

4. **Example 4:**
   - **Set:** \(\{ 4, 6, 8, 24, 78 \}\)
   - **Format:** Roster Notation
     - **Explanation:** The elements of this set, which are specific numbers, are listed explicitly. This direct listing is characteristic of roster notation.

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By correctly matching each set to its respective format, we gain a clearer understanding of how sets can be represented either by listing their elements (roster notation) or by describing the properties that their elements satisfy (set builder notation). This foundational skill is crucial for more advanced mathematical learning.
Transcribed Image Text:**Understanding Set Notations: An Educational Guide** In this section, we will explore sets written in two different formats and correctly identify the notation used for each example. This understanding is fundamental in set theory, helping to distinguish between methods of representing sets. 1. **Example 1:** - **Set:** \(\{ x \in A \mid x \text{ is even} \}\) - **Format:** Set Builder Notation - **Explanation:** This set describes all elements \( x \) in a certain set \( A \) where \( x \) is an even number. It uses a condition to define the set. 2. **Example 2:** - **Set:** \(\{ \text{dog, cat, fish, bearcat} \}\) - **Format:** Roster Notation - **Explanation:** This set lists its elements directly. The elements are specific animals, and the set is defined by explicitly enumerating its members. 3. **Example 3:** - **Set:** \(\{ \text{animal: the animal makes a good pet} \}\) - **Format:** Set Builder Notation - **Explanation:** This set uses a descriptive condition to include elements. Any animal that makes a good pet is part of the set, defined by the given property. 4. **Example 4:** - **Set:** \(\{ 4, 6, 8, 24, 78 \}\) - **Format:** Roster Notation - **Explanation:** The elements of this set, which are specific numbers, are listed explicitly. This direct listing is characteristic of roster notation. --- By correctly matching each set to its respective format, we gain a clearer understanding of how sets can be represented either by listing their elements (roster notation) or by describing the properties that their elements satisfy (set builder notation). This foundational skill is crucial for more advanced mathematical learning.
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