# Union and intersection

1. Jan 19, 2009

### dimpledur

1. The problem statement, all variables and given/known data

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

3. 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.

2. Jan 19, 2009

### NoMoreExams

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

3. Jan 19, 2009

### 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?

4. Jan 19, 2009

### 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)

5. Jan 19, 2009

### NoMoreExams

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

6. Jan 19, 2009

### 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?

7. Jan 19, 2009

### dimpledur

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

8. Jan 20, 2009

### 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 $$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$$.

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