Set language and notation：練習問題

Given that the universal set \( \xi = \{1, 2, 3, 4, 5, 6, 7, 8\} \) and set \( A = \{2, 4, 6, 8\} \), find the number of elements in the complement set \( A' \).

Given the universal set \( \xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \), set \( A = \{2, 4, 6, 8, 10\} \) and set \( B = \{3, 6, 9\} \), find the number of elements in the set \( (A \cup B)' \).

Given the universal set \( \xi = \{x \in \mathbb{Z} : 1 \le x \le 20\} \), set \( A = \{x : x \text{ is a multiple of 3}\} \), and set \( B = \{x : x \text{ is a square number}\} \). Find the number of elements in \( A \cup B \).

Let set \( P = \{x : x \text{ is a prime number and } 10 < x < 20\} \). Which of the following statements is true?

Consider the universal set \( \xi = \{x \in \mathbb{Z} : 1 \le x \le 15\} \).
Two sets are defined as follows:
\( A = \{x : x \text{ is a prime number}\} \)
\( B = \{x : x \text{ is a multiple of 3}\} \)
Find the number of elements in the set \( (A \cup B)' \).

The universal set \( \xi = \{x : x \text{ is an integer, } 1 \le x \le 10\} \).
Set \( A = \{2, 3, 5, 7\} \) and set \( B = \{x : x \text{ is a multiple of 3}\} \).
List the elements of the set \( A \cap B' \).