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Math Help - logic derivation

  1. #1
    Junior Member
    Joined
    Jul 2009
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    logic derivation

    Im stuck and cant seem to find a way to continue

    pr- ∀x(F(xa(x))→∼F(xx))
    show ∴ ∼∃x∀yF(a(x)y
    QN is disabled. Use UI, EI, and EG in the derivation

    1. show ∼∃x∀yF(a(x)y
    2. -------∃x∀yF(a(x)y) Ass id
    3.--------∀yF(a(i)y) 2 ei
    4.--------F(a(i)a(i)) 3 ui
    5.--------∀x(F(xa(x))→∼F(xx)) pr
    6.--------F(a(i)a(a(i)))→∼F(a(i)a(i)) 5 ui
    7---------∼∼F(a(i)a(i)) 4 dn
    8---------∼F(a(i)a(a(i))) 6 7 mt
    9 --------∃x∼F(xa(x)) 8 eg

    I dont know how to continue
    Any advice will be appreciated, Thnx
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  2. #2
    MHF Contributor
    Joined
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    Re: logic derivation

    You are almost there. Instead of step 9, instantiate ∀yF(a(i)y) from step 3 with a(a(i)). The result would contradict step 8.
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