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Exam 2 FormatExam 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 sheetrule sheet will be provided.
1 problem from Set D2 problem from Set E2 problems from Set F1 problem from Set G (91-96)
3
Inference Rules (so far)Inference Rules (so far)
––––
I
––––––
––––––
O
()––––––––
O––––––
––––––
I ––––––
––––––
O
–––––– &
–––––– &
&I & ––––––
& ––––––
&O
–––––
–––––
DN
()––––––––&
O
(&)––––––––
&O
5
SHOW-STRATEGIESSHOW-STRATEGIESThere are 6 kinds of formulas in Sentential Logic:
For each of these, there is
a suggested show-strategy.
1. atomic formulas P, Q, etc.
2. negations 3. conjunctions &
4. conditionals 5. disjunctions 6. biconditionals
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Show-Conjunction StrategyShow-Conjunction Strategy
: &&
: ° ° °
: ° ° °
&D
??
??
NEW RULENEW RULENEW STRATEGYNEW STRATEGY
11(12)
(11)
(10)
(9)
(8)
(7)
(6)
(5)
(4)
(3)
(2)
(1)
Example 1Example 1
11, R
1,9, Q & R
DD : RAs P
CD : P R6, Q
1,4, Q & R
DD : QAs P
CD : P Q&D: (P Q) & (P R)
PrP (Q & R)
&O
O
&O
O
12
(12)(13)(14)(15)
(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1) Example 2Example 2
As QDD : 2,12, P3,12, P
D : Q6,9, 3,8, P1,6, QDD : As PD : P&D: P & QPrQ PPrQ PPrP Q
(16) 14,15,
IOO
OOI
13(17)(16)
(12)(13)(14)(15)
(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1) Example 3Example 3
13,16, 4,15, P
ID : PAs PDD : 2,13, Q
7,10, 4,9, Q1,7, PDD : As QID : Q&D : Q & PAs P QCD: (P Q) (Q & P)PrP QPrP Q
IOO
IOO