https://file.aiquickdraw.com/mathbot/file/1729638680002w0pg633q.jpg

Let's break down and solve the questions based on the provided image:

### (a) Find the cardinalities of \( A \) and \( B \).

- Set \( A = \{d, e, f, g, h, i, j, k\} \) consists of 8 elements.
- Set \( B \) is defined as the set of odd numbers greater than 5 and less than 19. These numbers are:
  \[
  B = \{7, 9, 11, 13, 15, 17\}
  \]
  So, \( B \) has 6 elements.

Therefore:
- \( n(A) = 8 \)
- \( n(B) = 6 \)

### (b) Select true or false.

1. **\( j \in A \)**: True. \( j \) is one of the elements of \( A \).
2. **\( h \notin A \)**: False. \( h \) is an element of \( A \).
3. **\( -1 \in B \)**: False. \( B \) contains only positive odd numbers between 5 and 19, and \( -1 \) is not in this range.
4. **\( 15 \in B \)**: True. 15 is one of the elements of set \( B \).

### Summary of answers:
1. \( j \in A \): **True**
2. \( h \notin A \): **False**
3. \( -1 \in B \): **False**
4. \( 15 \in B \): **True**

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Would you like more details or clarification on any part of this solution?

Here are 5 related questions you might find interesting:
1. What is the difference between cardinality and membership in set theory?
2. How do you define even and odd numbers mathematically?
3. Can a set contain negative numbers? If so, give an example.
4. How do you calculate the union of two sets like \( A \) and \( B \)?
5. How can you visually represent sets \( A \) and \( B \) using a Venn diagram?

**Tip**: When working with set theory, it’s useful to carefully distinguish between elements that belong to a set (membership) and the total number of elements in the set (cardinality).

Find the cardinalities of sets A and B, and answer the true or false questions based on set membership.

Learn how to calculate the cardinalities of sets A and B, and solve related true/false questions based on set membership. Set A contains 8 elements, and Set B contains 6 odd numbers between 5 and 19. This problem is ideal for students in Grades 6-8.

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