# 2 set theory problems

1. Sep 2, 2012

### sbc824

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

show S1 U S2 = (S1' ∩ S2')'

3. The attempt at a solution

I'm pretty sure I have this right or I'm close

Let x ∈ S1 U S2
x ∈ S1 or x ∈ S2
Since x ∈ S1 or S2, then x ∉ S1' and S2'
If x ∉ S1' and S2', then x ∈ (S1' and S2')'
Therefore, S1 U S2 = (S1' ∩ S2')'

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

show S1 U S2 - (S1 ∩ S2') = S2

3. The attempt at a solution

I have not attempted this as I'm not sure how to start this one...any help would be appreciated.

Last edited: Sep 2, 2012
2. Sep 2, 2012

### SammyS

Staff Emeritus
You don't have the first part right.

3. Sep 2, 2012

### sbc824

wow silly mistake thanks...any starting hints for 2? I can easily visualize it with a diagram...but I'm rusty with set notation.

4. Sep 2, 2012

### SammyS

Staff Emeritus
Another problem with your solution to part 1 is that you have only shown that S1 U S2 ⊆ (S1' ∩ S2')' (that is, if you have truly corrected your proof). To show equality, you also need to show that S1 U S2 ⊇ (S1' ∩ S2')' .