# Discrete Math Proof

1. Oct 3, 2012

### Bashyboy

1. The problem statement, all variables and given/known data
Prove the complementation law in Table 1 by showing
that $\stackrel{=}{A} = A$

2. Relevant equations

3. The attempt at a solution

Well, first I assumed that x is an element of A, so that $A = (x | x\in A)$

by taking the complement, I got $(x | \neg(x\in A) \rightarrow (x | x\notin A)$

then, taking the complement of the complement is where I get stuck:

$(x | \neg(x \in \overline{A})$

2. Oct 3, 2012

### Bashyboy

I have another one:
Prove the domination laws in Table 1 by showing that
A ∪ U = U

A∪U = {x| x∈A∨x∈U} = {x| x∈ A ∨ T} = {x| T}=U

This is from the solution manual. I understand all but the last step. To me, the last step seems meaningless; how could you infer anything from it?

3. Oct 5, 2012

### Bashyboy

In my original post, the arrow should actually be an equal sign.