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Homework Help: Prove by natural deduction

  1. Jul 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove by natural deduction
    ((X [itex]\Rightarrow[/itex] ¬Y)[itex]\vee[/itex](¬X[itex]\Rightarrow[/itex]Y))[itex]\Rightarrow[/itex](¬(X[itex]\wedge[/itex]Y)[itex]\wedge[/itex]¬(¬X[itex]\wedge[/itex]¬Y))

    2. Relevant equations

    3. The attempt at a solution
    i understand basic natural deduction and how to prove via it but this one has me stumped as there is no [itex]\models[/itex] symbol which normally means that everything to the right is what you have to end up with using everything to the left of the [itex]\models[/itex] symbol

    Could really use some help here!!!!
  2. jcsd
  3. Jul 19, 2011 #2


    Staff: Mentor

    Is this the same problem you posted in the other thread?

    Occasionally someone will post a symbolic logic problem such as this, but as I recall, not many of the members here normally weigh in. Most of us here are better versed in mathematical logic, which uses different symbols, and is usually less theoretic and more applied.

    I don't suppose you could use a truth table? The expression on the left of the outer implication is a tautology; i.e., always true. Also, (X [itex]\Rightarrow[/itex] ¬Y) [itex]\Leftrightarrow[/itex] ¬(X[itex]\wedge[/itex]Y). Similarly, (¬X [itex]\Rightarrow[/itex] Y) [itex]\Leftrightarrow[/itex] ¬(¬X[itex]\wedge[/itex]¬Y). Hope this helps.
  4. Jul 19, 2011 #3
    yeah its the same as in the other thread but i managed to work out the resolution bit of it and it would not let me edit the post which looked rather cluttered
    Last edited: Jul 20, 2011
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