U = {x; 3 < x < 14}
A = {6, 7, 9, 10, 13}
B = {4, 5, 11}

A irisan B komplemen

To solve for the intersection of set \( A \) and the complement of set \( B \) within the universal set \( U \), we follow these steps:

### Step 1: Define the universal set \( U \)
The universal set \( U \) is the set of all real numbers \( x \) such that \( 3 < x < 14 \). Therefore:
\[
U = \{4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}
\]

### Step 2: Define sets \( A \) and \( B \)
- \( A = \{6, 7, 9, 10, 13\} \)
- \( B = \{4, 5, 11\} \)

### Step 3: Find the complement of set \( B \) in \( U \)
The complement of \( B \), denoted \( B^c \), is the set of all elements in \( U \) that are not in \( B \):
\[
B^c = U - B = \{6, 7, 8, 9, 10, 12, 13\}
\]

### Step 4: Find the intersection of \( A \) and \( B^c \)
Now, we compute the intersection \( A \cap B^c \), which is the set of elements that are both in \( A \) and in \( B^c \):
\[
A \cap B^c = \{6, 7, 9, 10, 13\} \cap \{6, 7, 8, 9, 10, 12, 13\}
\]
\[
A \cap B^c = \{6, 7, 9, 10, 13\}
\]

### Final Answer:
The intersection \( A \cap B^c = \{6, 7, 9, 10, 13\} \).

Would you like more details on this solution, or have any other questions?

Here are five related questions for further practice:
1. What is \( A \cup B \)?
2. What is \( B \cap A^c \)?
3. What is \( A^c \cup B^c \)?
4. What is \( (A \cup B)^c \)?
5. What is \( (A \cap B)^c \)?

**Tip:** When dealing with set complements, always remember to reference the universal set to ensure you include all elements not in the subset.

Learn how to find the intersection of set A and the complement of set B within the universal set U. This problem involves set theory concepts, including complement and intersection operations. Suitable for high school students studying set theory.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation