Proving Set Stuff: Reconstructing Equations w/ Different Assumption

[1MileCrash]

Homework Statement

My teacher gave us the following proofs:

(AUB)' = A'n B'
x is in (AUB)'
x is not in AUB
x is not in A and x is not in B
x is in A' and x is in B'

Therefore, x is in A'n B'

(A n B)' = A' U B'

x is in A'UB'
Therefore x is in A' or x is in B'
therefore x is not in A or x is not in B
Therefore is in (A n B)'

(I used U for union, n for intersection.)

I am asked to reconstruct them using the other initial assumption about X (assume it's in the other group instead)

Homework Equations

The Attempt at a Solution

(AUB)' = A'n B'

is in A' n B'
x is not in A and x is not in be.
x is in A' and x is in B'

How can I get to the other set, which is a union/or?

 

[micromass]

(AUB)' = A'n B'

is in A' n B'
x is not in A and x is not in be.

Next line: x is not in A or in B.
Then: ...

 

[1MileCrash]

Ahh, that's pretty much the end. So x is in (AUB)' by that alone. Thanks! I'll work on the other one and come back if I need help.

 

[1MileCrash]

My work for the second:

(A n B)' = A' U B'

x is in (A n B)'
x is not in (A n B)
x is not in A or x is not in B
x is in A' or x is in B'
x is in A' U B'

 

[micromass]

That's ok!