# Homework Help: Number of elements for a given probability?

1. Oct 30, 2012

### V0ODO0CH1LD

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

Let A be a set with 8 elements and B be a set such that A U B has 12 elements. What is the number of elements in P(B\A) U P(∅)?

2. Relevant equations

3. The attempt at a solution

I have no idea what it means to ask what are the number of elements in a probability.. Is it the number of elements that would represent that probability?

Last edited: Oct 30, 2012
2. Oct 30, 2012

### tiny-tim

Hi V0ODO0CH1LD!
That P is (probably) the power set, the set of all subsets of the thing inside the brackets.

(see http://en.wikipedia.org/wiki/Power_set)

3. Oct 30, 2012

### V0ODO0CH1LD

Okay, I red about power sets but I couldn't find anything on how to operate with them.

Also, can I say that |A U B| = |A| + |B| - |A(intersect)B|?
Because then I could say 12 = 8 + |B| - |A(intersect)B|
Which would imply that 4 = |B| - |A(intersect)B| = |B\A|
And that would mean that P(B\A) U P(∅) = 2^4 + 1 = 17

Is that correct?

4. Oct 30, 2012

### tiny-tim

Yup! |(B\A)| = 4, so P(B\A) = 24, and P(∅) = 20 = 1

(but do they intersect? )

5. Oct 30, 2012

### V0ODO0CH1LD

Thanks a lot!! I would think they don't intersect because if |(B\A)| = 4 and |A U B| = 12 and |A| = 8 then that means |B| = 4.

6. Oct 30, 2012

### tiny-tim

No, i mean, do P(B\A) and P(∅) intersect?

7. Oct 30, 2012

### V0ODO0CH1LD

Ohh!! So the answer is actually 16??

8. Oct 30, 2012

### tiny-tim

Probably!

9. Oct 30, 2012

Ha! Thanks!