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Discrete Math Proof

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove the complementation law in Table 1 by showing
    that [itex]\stackrel{=}{A} = A[/itex]


    2. Relevant equations



    3. The attempt at a solution

    Well, first I assumed that x is an element of A, so that [itex]A = (x | x\in A)[/itex]

    by taking the complement, I got [itex](x | \neg(x\in A) \rightarrow (x | x\notin A)[/itex]

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

    [itex](x | \neg(x \in \overline{A}) [/itex]
     
  2. jcsd
  3. Oct 3, 2012 #2
    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?
     
  4. Oct 5, 2012 #3
    In my original post, the arrow should actually be an equal sign.
     
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