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INTRO LOGIC

INTRO LOGIC. Derivations in SL 5. DAY 13. Exam 2 Format. 6 argument forms, 15 points each, plus 10 free points Symbolic argument forms (no translations) For each one, you will be asked to construct a derivation of the conclusion from the premises. The rule sheet will be provided.

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INTRO LOGIC

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  1. INTRO LOGIC Derivations in SL5 DAY 13

  2. Exam 2 Format • 6 argument forms, 15 points each, plus 10 free points • Symbolic argument forms (no translations) • For each one, you will be asked to construct a derivation of the conclusion from the premises. • The rule sheet will be provided. • 1 problem from Set D • 2 problem from Set E • 2 problems from Set F • 1 problem from Set G (91-96)

  3. Inference Rules (so far) &O (&) ––––––––   &O & ––––––  & ––––––  &I   –––––– &   –––––– & O   ––––––    ––––––  I  ––––––   ––––––  O () ––––––––   O   ––––––    ––––––  O () –––––––– & DN  –––––   –––––  I   –––– 

  4.  Rules (so far) DD : DD     CD : CDAs:    D : DAs:     ID : IDAs:    

  5. SHOW-STRATEGIES • There are 6 kinds of formulas in Sentential Logic: 1. atomic formulas P, Q, etc. 2. negations  3. conjunctions & 4. conditionals  5. disjunctions  6. biconditionals  For each of these, there is a suggested show-strategy.

  6. Show-Conditional Strategy • :  •  As • :  • ° • ° • ° CD ??

  7. Show-Negation Strategy • :  •  As • :  • ° • ° •  D DD

  8. Show-Atomic Strategy • :  •  As • :  • ° • ° •  ID DD  is atomic (P,Q,R, etc.)

  9. Show-Disjunction Strategy • :  • [] As • :  • ° • ° •  ID DD

  10. Show-Conjunction Strategy &D • : & • :  • ° • ° • ° • :  • ° • ° • ° ?? ?? NEW RULENEW STRATEGY

  11. Example 1 (1) P  (Q & R) Pr (2) : (P  Q) & (P  R) &D (3) : P  Q CD (4) P As (5) : Q DD (6) Q & R 1,4, O (7) Q 6, &O (8) : P  R CD (9) P As (10) : R DD (11) Q & R 1,9, O (12) R 11, &O

  12. Example 2 (1) P  Q Pr (2) Q  P Pr (3) Q P Pr (4) : P & Q &D (5) : P D (6) P As (7) :  DD (8) Q 1,6, O (9) P 3,8, O (10)  6,9, I (11) : Q D (12) Q As (13) :  DD (14) P 2,12, O (15) P 3,12, O (16)  14,15, I

  13. Example 3 (1) P  Q Pr (2) P Q Pr (3) : (P  Q)  (Q & P) CD (4) P  Q As (5) : Q & P &D (6) : Q ID (7) Q As (8) :  DD (9) P 1,7, O (10) Q 4,9, O (11)  7,10, I (12) : P ID (13) P As (14) :  DD (15) Q 2,13, O (16) P 4,15, O (17)  13,16, I

  14. THE END

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