Solving Union and Intersection Expressions

[dimpledur]

Homework Statement

Simplify the expression: (B union C) intersection (B union NOT-C) intersection (NOT-B union C)

The Attempt at a Solution

I have no clue how to attempt this question, as every time I do attempt it I get a different solution.

 

[NoMoreExams]

Show some work that you've done where you are getting different answers

 

[dimpledur]

Well, I can't really show you my work because I don't know how to do it without ven diagrams. Is there another way?

 

[dimpledur]

Perhaps if I tell you what my final solution was, you could just tell me if I did it right?

My simplified version was (B intersection C)

 

[NoMoreExams]

You can see if your method is correct by doing the "element-chasing-method". Have you tried verifying your answer that way?

 

[dimpledur]

Okay, I just tried using elements, and it turns out that there is no simplified version of that expression. Or would the simplified expression be nothing? ie. an empty set?

 

[dimpledur]

or should I write "null" at the bottom of my solution?

 

[wsalem]

Your simplified result $$B \cap C$$ is correct nonetheless, but you may need to do it without Venn diagrams!
Apply the associativity and distributivity laws. You have $$A \cap (B \cap C) = (A \cap B) \cap C$$, similarly for unions. And $$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$$ and $$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$$.