Mccarthy O'Quinn
01/16/2023 · Elementary School
\( ( A \cup B ) \cap ( B \cup C ) \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( ( A \cup B ) \cap ( B \cup C ) \), we can use the properties of set operations.
1. **Distributive Law**: The intersection distributes over the union. We can rewrite the expression as follows:
\[
( A \cup B ) \cap ( B \cup C ) = ( A \cap ( B \cup C )) \cup ( B \cap ( B \cup C ))
\]
2. **Simplifying \( B \cap ( B \cup C ) \)**: Since \( B \) is a subset of \( B \cup C \), we have:
\[
B \cap ( B \cup C ) = B
\]
3. **Now substituting back**: We can substitute this back into our expression:
\[
( A \cup B ) \cap ( B \cup C ) = A \cap ( B \cup C ) \cup B
\]
4. **Final Expression**: The final simplified expression is:
\[
( A \cup B ) \cap ( B \cup C ) = ( A \cap ( B \cup C )) \cup B
\]
This means that the result of the intersection of the two unions is the union of the intersection of \( A \) with \( (B \cup C) \) and the set \( B \).
In summary, the simplified form of \( ( A \cup B ) \cap ( B \cup C ) \) is:
\[
( A \cap ( B \cup C )) \cup B
\]
Quick Answer
\( ( A \cap ( B \cup C )) \cup B \)
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
(0)
Ask Real Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
PREV 
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
