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.