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Help understanding the proof of De Morgan's Law

  1. Jul 12, 2009 #1
    I need some help on understanding the proof of De Morgan's Law.

    (A intersection B)' = A' U B'
    I know that it is proof is along the lines of

    Let x be in (A intersection B)'.
    Then x is NOT in A intersection B
    <=> x not in A AND x not in B (use logical connectors, negations, etc)
    <=> x in A' OR x in B'
    <=> x in A' U B'

    but my question is how does the AND become an OR?
     
  2. jcsd
  3. Jul 12, 2009 #2

    HallsofIvy

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    The statement "I am going to work AND I am going to have pizza for lunch" is true only if BOTH are true. If I want to show "It is NOT true that I am going to work and I going to have pizza for lunch" I only need to show ONE of those two if false. That is, either I am NOT going to work or I am NOT going to have pizza for lunch. I don't have to show that they are both false, only that they are not both false. "Not A and B" is the same as "not A or not B".
     
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