https://file.aiquickdraw.com/mathbot/file/1725712896991h776rave.jpg

Define the sets A, B, C, and D as shown. **Select all statements which are true.**   Question 19 options:

D ⊆ B

{g, m, p, s} ⊆ B

{a, p, s, w} ⊂ A

{a, f, g, h, m, p} ⊆ B

{m, s} ⊆ C

Let's analyze the Venn diagram in the image and check which statements are true.

### **Definitions of the Sets:**
- **Set A**: Includes elements: \( w, c, l, s, m, p \)
- **Set B**: Includes elements: \( a, g, f, h, p \)
- **Set C**: A subset of \( A \), includes elements: \( s, m \)
- **Set D**: A subset of \( B \), includes elements: \( a, g, f, h \)

### **Now, evaluate the statements:**

1. **\( D \subseteq B \)**:  
   Set \( D \) includes elements \( a, g, f, h \), and these elements are all within \( B \).  
   **True**

2. **\( \{g, m, p, s\} \subseteq B \)**:  
   Elements \( g, p \) are in \( B \), but \( m \) and \( s \) are not.  
   **False**

3. **\( \{a, p, s, w\} \subset A \)**:  
   Set \( A \) contains \( w, s, p \), but not \( a \).  
   **False**

4. **\( \{a, f, g, h, m, p\} \subseteq B \)**:  
   Set \( B \) contains \( a, f, g, h, p \), but not \( m \).  
   **False**

5. **\( \{m, s\} \subseteq C \)**:  
   Set \( C \) contains both \( m \) and \( s \).  
   **True**

### **Final List of True Statements:**
- **\( D \subseteq B \)**
- **\( \{m, s\} \subseteq C \)**

Would you like further clarification or details on any of these statements?

---

Here are 5 related questions to further explore Venn diagrams and set theory:
1. How can you determine the intersection of two sets using a Venn diagram?
2. What is the difference between a subset and a proper subset?
3. How can you find the union of two or more sets?
4. How do you prove that one set is a subset of another?
5. What does the complement of a set represent in set theory?

**Tip**: Always ensure each element in a set matches exactly to avoid confusion between subsets and supersets.

Define the sets A, B, C, and D as shown. **Select all statements which are true.** Question 19 options: D ⊆ B, {g, m, p, s} ⊆ B, {a, p, s, w} ⊂ A, {a, f, g, h, m, p} ⊆ B, {m, s} ⊆ C.

Explore the relationships between sets A, B, C, and D using a Venn diagram. This problem involves identifying which subsets are true based on the provided diagram, testing your understanding of set theory and proper subsets. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation