Set Theory Problems | Mathix (MathGPT)

Power Set Subsets

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

Set Operations

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

Set Operations

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

Set Operations

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

Set Operations

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

Set Operations

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

Set Elements

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

Set Union Intersection

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

Set Union

1. **Problem Statement:** Find the union of sets $A$ and $B$ where $A = \{0, 4, 8, 12\}$ and $B = \{0, 3, 6, 9, 12\}$. 2. **Formula and Explanation:** The union of two sets $A$ and

Set Operations

1. **Problem Statement:** Find the intersections and unions of the given sets. 2. **Recall the definitions:**

Set Union

1. The problem involves finding the union of sets $A$ and $Y$, denoted as $A \cup Y$. 2. Recall that the union of two sets $A$ and $Y$ is the set containing all elements that are i

Venn Set Difference

1. ปัญหาคือการหาว่าส่วนที่แรเงาในแผนภาพ Venn ของเซต A, B, C และ U แทนเซตใดในตัวเลือกที่ให้มา 2. เรามีเซต U เป็นเอกภพสัมพัทธ์ และ A, B, C เป็นสับเซตของ U

Set Operations

1. **State the problem:** Find the intersections and unions of given sets. 2. **Recall set operations:**

Power Set Union

1. ปัญหาคือหาจำนวนสมาชิกของเซต $P(P(A)) \cup P(A)$ โดยที่ $A = \{\emptyset, \sqrt{2}\}$ 2. เริ่มจากหาขนาดของเซต $A$ ซึ่งมีสมาชิก 2 ตัว คือ $\emptyset$ และ $\sqrt{2}$ ดังนั้น $|A| =

Venn Diagram Shapes

1. **Problem Statement:** We have a Venn diagram with three circles A, B, and C containing various colored shapes. We need to:

Cartesian Product Intersection

1. **Problem Statement:** Prove that for the sets

Set Differences

1. **State the problem:** Given sets A and B with $n(A) = 17$, $n(A \cup B) = 38$, and $n(A \cap B) = 2$, find $n(A - B)$, $n(B)$, and $n(B - A)$. 2. **Recall formulas and rules:**

Set Operations

1. **Problem statement:** Given sets $U = \{x \mid x \in \mathbb{N}, x \leq 10\}$,

Students Only Maths

1. **Problem Statement:** We are given that 30 students like Maths, 25 like Science, and 10 like both Maths and Science. We need to find how many students like only Maths. 2. **For

Color Intersection

1. **Problem statement:** In a class, 65% of students like green (G), 45% like blue (B), and some like both. We need to find the percentage who like both colors. 2. **Formula used:

Src Voting

1. **State the problem:** We have 100 voters choosing among three candidates: Akayuure (A), Manukre (M), and Odonti (O). We want to find the number of voters who preferred all thre