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Proof Question

  1. Dec 6, 2014 #1
    1. The problem statement, all variables and given/known data
    Hypotheses: not a, b or not c, b→ (a and d), e→(c)

    Conclusion: not e

    2. The attempt at a solution:

    So far, I have this: 1) not a as premise

    2) b or not c as premise

    3) b→ (a and d) as premise

    4) e→(c) as premise

    5) a by Step 1 and Law of Excluded Middle.

    6) c is true by Step 5 and 4 a and e→c and Modus Ponens.

    7) c→b is true by Step 2 and implication.

    8) b→a and b→d by Step 3.

    I am unsure of what my next step(s) should be. I feel that it may be ((e implies c) and not c) implies not e) (Modus Tollens). I maybe should have 9) not c by Step 6 and Law of Excluded Middle. And then 10) ((e implies c) and not c) implies not e) (Modus Tollens).

     
  2. jcsd
  3. Dec 6, 2014 #2
    please explain your point 5). It's wrong, but I want to know what your reasoning was.
     
  4. Dec 6, 2014 #3
    I actually see my mistake. I was thinking of Law of Excluded Middle, but that actually states x or not x which means that my point was wrong.
     
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