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Help with indirect logic proof please!

  1. Mar 28, 2012 #1
    Using the five axioms below prove: p→q

    A1: p→~y
    A2: ~r→q
    A3: p→~z
    A4: x→ q or z
    A5: r→x or y

    Do I have to take the contrapositive of some of the axioms to begin this proof?
  2. jcsd
  3. Mar 28, 2012 #2


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    Science Advisor

    Yes, that would be the simplest thing to do. The very first "axiom" gives you p-> ~y but there is no "~y-> " so you cannot continue directly. However, you do have "A5: r->x or y which has contrapositive ~(x or y)= (~x) and (~y)->~r and then both "A2: ~r-> q" and "A4: x-> q or z".
  4. Mar 28, 2012 #3
    Am I on the right track with this?

    Conclusions Justifications
    1. p Given
    2. ~z or ~y All cases
    3. ~z Case 1
    4. ~x A4
    5. ~r A5
    6. q A2
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