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Validity SD Logic Homework Question

  1. Nov 13, 2008 #1
    Show that the following argument is valid in SD.
    (I will use "⊃" to show conditional.)

    Code (Text):
    (E v (L v M)) & (E ≡ F)
    L ⊃ D
    D ⊃ ~ L
    ----------------------
    E v M
    I'm only allowed to use the basic derivation rules of SD:
    Code (Text):
    Reiteration (R)
    Conjunction Intro. (&I) and Conjunction Elim. (&E)
    Conditional Intro. (⊃I) and Conditional Elim. (⊃E)
    Negation Intro. (~I) and Negation Elim. (~E)
    Disjunction Intro. (vI) and Disjunction Elim. (vE)
    Biconditional Intro. (≡I) and Biconditional Elim. (≡E)
     
    My attempts at a solution have not been very successful, but this is what I have come up with so far:

    Code (Text):
    1. (E v (L v M)) & (E ≡ F) [assumption]
    2. L ⊃ D [assumption]
    3. D ⊃ ~ L [assumption]
    ------
    4. ~(E v M) [subproof1open: assumption]
    ---
    5. L [subproof2open: assumption]
    ---
    6. L [subproof2close: 5R]

    7. M [subproof2open: assumption]
    ---
    8. ~L [subproof3open: assumption]
    ---
    9. L [subproof3: ????]
    10. ~ L [subproof3close: 8R]
    11. L [subproof2close: 8-10~E]
    12. D [subproof1: 3-13⊃E]
    13. L [subproof1: 5-6,7-11vE]
    14. ~ L [subproof1close: 3-12⊃E]
    15. E v M [4-14~E]
    Any help at all would be great, thanks in advance.
     
  2. jcsd
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