Number of elements for a given probability?

[V0ODO0CH1LD]

Homework Statement

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(∅)?

Homework Equations

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?

 

[tiny-tim]

Hi V0ODO0CH1LD!

… What is the number of elements in P(A\B) U P(∅)?

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)

 

[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?

 

[tiny-tim]

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

(but do they intersect? )

 

[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.

 

[tiny-tim]

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

 

[V0ODO0CH1LD]

Ohh! So the answer is actually 16??

 

[tiny-tim]

Probably!

 

[V0ODO0CH1LD]

Ha! Thanks!