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Homework Help: Prove by both Natural Deduction and Resolution

  1. Jul 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Prove by both natural deduction and by resolution
    ((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
    as far as natural deduction on this goes i have no idea since there is no ' I- ' looking symbol so im clueless

    i also got a bit stuck on the resolution this is what i have so far

    ¬(((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)))

    - ((X [itex]\Rightarrow[/itex] ¬Y)[itex]\vee[/itex](¬X[itex]\Rightarrow[/itex]Y))[itex]\wedge[/itex](¬(X[itex]\wedge[/itex]Y)[itex]\wedge[/itex]¬(¬X[itex]\wedge[/itex]¬Y))
    - ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex]¬(¬(X[itex]\wedge[/itex]Y)[itex]\wedge[/itex]¬(¬X[itex]\wedge[/itex]¬Y))
    - ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex]¬(¬(X[itex]\wedge[/itex]Y)[itex]\wedge[/itex]¬(¬X[itex]\wedge[/itex]¬Y))
    - ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex]¬((¬X[itex]\vee[/itex]¬Y)[itex]\wedge[/itex](X[itex]\vee[/itex]Y))
    - ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex]¬(¬X[itex]\vee[/itex]¬Y)[itex]\vee[/itex]¬(X[itex]\vee[/itex]Y)
    - ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex](X[itex]\wedge[/itex]Y)[itex]\vee[/itex]¬(X[itex]\vee[/itex]Y)
    - ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex](X[itex]\wedge[/itex]Y)[itex]\vee[/itex](¬X[itex]\wedge[/itex]¬Y)

    then i dont know what do as it gets stuck i probably did something wrong somewhere i can see that i screwed up my latez on the left hand side i know its (¬X v ¬Y v X v Y) not (¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y) its the right hand side which i got stuck on
    Last edited: Jul 18, 2011
  2. jcsd
  3. Jul 19, 2011 #2
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