# Help with (a-b)'=b'-a'

1. Nov 16, 2008

### kathrynag

1. The problem statement, all variables and given/known data
Prove or disprove:

(A-B)'=B'-A'

2. Relevant equations

3. The attempt at a solution
Let x$$\in$$(A-B)'
Then x$$\notin$$(A-B)
I'm not sure where to go from here...

2. Nov 16, 2008

### Staff: Mentor

Re: (a-b)'=b'-a'

What's the context here? What are A and B? What does (A - B)' mean?

3. Nov 16, 2008

### VeeEight

Re: (a-b)'=b'-a'

A-B is the set of elements in A that are not in B
So x is not in A-B means that x is in A but is not in B

You may want to try to think of some counterexamples before trying to show inclusion both ways.

4. Nov 16, 2008

### kathrynag

Re: (a-b)'=b'-a'

Ok so:
x$$\in$$A and x$$\notin$$B

Ok, so suppose A={1,2,3,4,5} B={3,4,6}
Then A-B={1,2,5}
So, (A-B)'={3,4,6}
so, (A-B)'=B

5. Nov 16, 2008

### VeeEight

Re: (a-b)'=b'-a'

If you are working in R, then the complement of the set A-B would be R - {1, 2, 5}
You might want to try some simpler examples like A= (0,1) or {1, 2, 3} and B = [0,1] or {3, 4}

6. Nov 16, 2008

### kathrynag

Re: (a-b)'=b'-a'

A={1,2,3}
B={3,4}
universe ={1,2,3,4,5,6,7}
A-B={1,2}
(A-B)'={3,4,5,6,7}

7. Nov 16, 2008

### VeeEight

Re: (a-b)'=b'-a'

Okay.

8. Nov 16, 2008

### kathrynag

Re: (a-b)'=b'-a'

So, if x is not an element of A-B, then x is not an element of {1,2}

9. Nov 16, 2008

### kathrynag

Re: (a-b)'=b'-a'

Ok, so

x$$\in$${3,4,5,6,7}
So x$$\notin$$A and x$$\in$$B

10. Nov 17, 2008

Re: (a-b)'=b'-a'

Keep going! What are A' , B' and B'-A' ?

11. Nov 17, 2008

### kathrynag

Re: (a-b)'=b'-a'

a'={4,5,6,7}
b'={1,2,5,6,7}
b'-a'={1,2}

12. Dec 2, 2008

### kathrynag

Re: (a-b)'=b'-a'

Still not quite sure
Let x$$\in$$(A-B)'
x$$\notin$$(A-B).
Can I say now x$$\in$$B? this is the part that confuses me...