1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook