集合語言、符號與子集：練習題

If set \(P = \{a, b, c, d\}\) and set \(Q = \{c, d, e, f\}\), find the intersection \(P \cap Q\).

In a group of 40 students, 25 students study Art, 18 students study Music, and 8 students study both subjects. Find the number of students who study neither Art nor Music.

The universal set \(\mathscr{E} = \{x : 1 \le x \le 12, x \in \mathbb{Z}^+\}\).
Set \(A = \{\text{multiples of 3}\}\).
Set \(B = \{\text{factors of 12}\}\).
Find the elements of the set \((A \cup B)'\).

The universal set \( \mathscr{E} = \{x : 1 \le x \le 15, x \in \mathbb{Z}^+\} \).
Set \( A = \{x : x \in \mathscr{E}, x \text{ is even}\} \)
Set \( B = \{x : x \in \mathscr{E}, x \text{ is a multiple of 3}\} \)
Find \( n(A \cup B) \).

In a group of 80 students, 45 study French (\(F\)), 35 study German (\(G\)), and 12 study both. Find the value of \(n(F \cup G)'\).

The universal set \(\mathscr{E} = \{x : 1 \le x \le 15, x \in \mathbb{Z}^+\}\).
Set \(S\) is the set of square numbers and set \(F\) is the set of factors of 12.
List the members of the set \(S \cap F\).

In a group of 40 students, 25 study Art (\( A \)), 20 study Music (\( M \)), and 8 study neither Art nor Music. Find the number of students who study both subjects, \( n(A \cap M) \).

Given the universal set \( \mathcal{E} = \{x : 1 \le x \le 12, x \in \mathbb{Z}\} \) and set \( B = \{x : x \text{ is a factor of 12}\} \), find the value of \( n(B) \).

In a survey of 40 students, 25 students study History (H) and 20 students study Geography (G). There are 8 students who study both subjects.
(a) Complete the Venn diagram to represent this information.
(b) Find the number of students who study History but not Geography.
(c) Determine \(n(H \cup G)'\).