S={1,2,3,...,18,19,20}
Let sets A and B be subsets of S, where:

Set A={3,8,10,11,12,13,16,17,19}

Set B={2,3,4,6,8,12,19,20}

You have defined two sets \( A \) and \( B \) as subsets of the set \( S = \{1, 2, 3, \dots, 20\} \), where:

- \( A = \{3, 8, 10, 11, 12, 13, 16, 17, 19\} \)
- \( B = \{2, 3, 4, 6, 8, 12, 19, 20\} \)

Here are some key set operations we can perform with these sets:

### 1. **Union** of A and B:
The union \( A \cup B \) is the set of all elements that are in either \( A \), \( B \), or both. This operation combines the elements of both sets without duplication.

\[
A \cup B = \{2, 3, 4, 6, 8, 10, 11, 12, 13, 16, 17, 19, 20\}
\]

### 2. **Intersection** of A and B:
The intersection \( A \cap B \) is the set of all elements that are in both \( A \) and \( B \).

\[
A \cap B = \{3, 8, 12, 19\}
\]

### 3. **Difference** \( A - B \):
The difference \( A - B \) is the set of all elements that are in \( A \) but not in \( B \).

\[
A - B = \{10, 11, 13, 16, 17\}
\]

### 4. **Difference** \( B - A \):
The difference \( B - A \) is the set of all elements that are in \( B \) but not in \( A \).

\[
B - A = \{2, 4, 6, 20\}
\]

### 5. **Symmetric Difference** of A and B:
The symmetric difference \( A \Delta B \) is the set of elements that are in either \( A \) or \( B \), but not in both. This can be calculated as \( (A - B) \cup (B - A) \).

\[
A \Delta B = \{2, 4, 6, 10, 11, 13, 16, 17, 20\}
\]

---

Would you like more details or have any questions about these operations?

Here are 5 related questions to explore further:

1. What is the complement of set \( A \) in \( S \)?
2. What is the complement of set \( B \) in \( S \)?
3. What is the cardinality (size) of each set: \( A \), \( B \), and their union \( A \cup B \)?
4. What is \( (A \cap B)^c \) (the complement of the intersection of \( A \) and \( B \) in \( S \))?
5. How would the operations change if sets \( A \) and \( B \) were defined over a different universal set?

**Tip:** To compute intersections and unions efficiently, remember that sets are unordered collections and thus do not consider repeated elements!

Let sets A and B be subsets of S={1,2,3,...,18,19,20} where Set A={3,8,10,11,12,13,16,17,19} and Set B={2,3,4,6,8,12,19,20}.

Explore set operations including union, intersection, and difference using subsets A and B of the set S={1,2,...,20}. This problem covers fundamental concepts in set theory, with detailed solutions and explanations. Ideal 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