Determine the cardinality of the following sets.
A={1,3,9,12,15,18,24} 
B={0,2,4,…………20} 
C={}
D={5,5,5,5,5} 
E={R,E,M,E,M,B,E,R}

Let's determine the cardinality of each set:

1. **Set A**:  
   \[
   A = \{1, 3, 9, 12, 15, 18, 24\}
   \]  
   The set \( A \) has 7 distinct elements.  
   **Cardinality of \( A \):** 7.

2. **Set B**:  
   \[
   B = \{0, 2, 4, \dots, 20\}
   \]  
   This set contains all even numbers from 0 to 20, inclusive. These elements are \(0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20\), giving 11 distinct elements.  
   **Cardinality of \( B \):** 11.

3. **Set C**:  
   \[
   C = \{\}
   \]  
   \( C \) is an empty set, containing no elements.  
   **Cardinality of \( C \):** 0.

4. **Set D**:  
   \[
   D = \{5, 5, 5, 5, 5\}
   \]  
   Although the number 5 appears multiple times, a set only considers unique elements. Therefore, \( D = \{5\} \), containing a single unique element.  
   **Cardinality of \( D \):** 1.

5. **Set E**:  
   \[
   E = \{R, E, M, E, M, B, E, R\}
   \]  
   After removing duplicates, \( E = \{R, E, M, B\} \), which contains 4 unique elements.  
   **Cardinality of \( E \):** 4.

### Summary of Cardinalities:
- \( |A| = 7 \)
- \( |B| = 11 \)
- \( |C| = 0 \)
- \( |D| = 1 \)
- \( |E| = 4 \)

Would you like further explanation on any of these steps?

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Here are five related questions for additional practice:

1. How do we determine the cardinality of the union of two sets?
2. If a set has repeating elements, how does that affect its cardinality?
3. What is the cardinality of the set of all odd numbers from 1 to 19?
4. How does the concept of an empty set differ from a set with one element?
5. Can a set have infinite cardinality? Provide an example.

**Tip:** Remember, in set theory, elements in a set are always unique, meaning duplicates do not affect the count of elements.

Determine the cardinality of the following sets. A={1,3,9,12,15,18,24} B={0,2,4,…………20} C={} D={5,5,5,5,5} E={R,E,M,E,M,B,E,R}

Learn how to determine the cardinality of sets with distinct and repeated elements. This solution explores the number of unique elements in each set: A={1,3,9,12,15,18,24}, B={0,2,4,…,20}, C={}, D={5,5,5,5,5}, and E={R,E,M,E,M,B,E,R}. Suitable for Grades 6-8.

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