📘 set theory

1. **Problem Statement:** (a) Shade the set $A' \cup B'$ where $A'$ and $B'$ are complements of sets $A$ and $B$ respectively.

1. **Problem Statement:** We have three music preferences among students: Jazz, Reggae, and Funk. Given:

1. **Problem 1:** Given sets $A = \{1, 3, 6, 8, 9, 12, 15\}$ and $B = \{6, 9, 12\}$, determine which statement is true: - (A) $B \subset A$

1. Problem 1: A school sports team has 68 students with overlapping participation in field, track, and swimming events. 2. Given:

1. **Stating the problem:** We have three sets:

1. The problem involves understanding the Cartesian product of sets $A$ and $B$, denoted as $A \times B = \{(x,y) : x \in A, y \in B\}$. 2. The notation $u(A) \times u(B) = q = (A

1. **Problem Statement:** List all subsets for the given sets and find the number of subsets for each.

1. **Problem Statement:** Given a universal set $U$ with $n(U) = 10$ and a subset $A = \{2, 4, 6\}$, find the number of elements in the complement of $A$, denoted $n(A')$. 2. **For

1. **Stating the problem:** We are given several sets and set operations to analyze and simplify using set theory rules.

1. **State the problem:** Prove the set equality $$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$$ using the set inclusion method. 2. **Recall the set inclusion method:** To prove

1. نبدأ ببيان المسألة: نريد إثبات هويتين لمجموعات ثلاث هي $X$, $Y$, و $Z$. 2. إثبات (a):

1. **Problem Statement:** Determine which of the given set identities is true for all sets $S$ and $T$. 2. **Recall important set theory rules:**

1. **Problem Statement:** Determine which of the given set identities is true for all sets $S$ and $T$. 2. **Recall important set theory rules:**

1. **Problem:** Given $S = \{1\}$, determine which of the following is *not* a subset of the power set $P(S)$. The options are: A) $\emptyset$

1. **Stating the problem:** We are given three sets:

1. The problem involves finding the union and intersection of sets A, B, and C. 2. Recall the definitions:

1. **Stating the problem:** We are given three sets: $$A = \{0, 4, 8, 12\}, B = \{0, 3, 6, 9, 12\}, C = \{-4, 4, 8\}$$

1. **Problem Statement:** Find the union and intersection of sets A, B, and C given:

1. **Problem Statement:** We are given three sets: $$A = \{0, 4, 8, 12\}, \quad B = \{0, 3, 6, 9, 12\}, \quad C = \{-4, 4, 8\}$$

1. **Problem statement:** Given sets $A$ and $B$ with $|A \cup B| = 166$ and $|A \cap B| = 74$, and the number of elements in $A$ is 12 more than in $B$. Find the number of element

1. **Problem Statement:** Find the union and intersection of the given sets: Sets: