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Let's work through this step by step.

### (a) Cardinalities of sets \( A \) and \( B \)

- Set \( A = \{20, 21, 22, 23, 24, 25\} \), which has 6 elements.
  - So, \( n(A) = 6 \).

- Set \( B \) is defined as the set of integers greater than or equal to \(-4\) and less than or equal to \(0\). This means \( B = \{-4, -3, -2, -1, 0\} \), which has 5 elements.
  - So, \( n(B) = 5 \).

Thus:
- \( n(A) = 6 \)
- \( n(B) = 5 \)

### (b) True or False questions

- **29 ∈ A**: False, since 29 is not in the set \( A \).
- **0 ∈ B**: True, since 0 is an element of set \( B \).
- **23 ∈ A**: True, since 23 is in set \( A \).
- **4 ∉ B**: True, since 4 is not in set \( B \).

### Final Answers:
1. (a) \( n(A) = 6 \), \( n(B) = 5 \)
2. (b) The correct answers are:
   - 29 ∈ A: False
   - 0 ∈ B: True
   - 23 ∈ A: True
   - 4 ∉ B: True

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Here are some related questions to explore further:
1. What does the term "cardinality" mean in set theory?
2. How can we define a set using inequalities?
3. How do you determine if an element belongs to a set?
4. What would be the cardinality of a set of real numbers between two values?
5. How do sets and subsets differ?

**Tip:** Remember, the notation \( ∈ \) means "is an element of," while \( ∉ \) means "is not an element of."

Let sets A and B be defined as follows. A = {20, 21, 22, 23, 24, 25}. B is the set of integers greater than or equal to -4 and less than or equal to 0. (a) Find the cardinalities of A and B. (b) Select true or false for each statement: 29 ∈ A, 0 ∈ B, 23 ∈ A, 4 ∉ B.

Solve a set theory problem involving sets A = {20, 21, 22, 23, 24, 25} and B = integers from -4 to 0. Learn how to find cardinalities and evaluate membership of elements in the sets. Suitable for Grades 6-8.

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