ΠΛΗ20 ΕΝΟΤΗΤΑ 2: ΠΡΟΤΑΣΙΑΚΗ ΛΟΓΙΚΗ Μάθηµα 2.2: Ταυτολογική Συνεπαγωγή ∆ηµήτρης Ψούνης
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20 2:
2.2:
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1.
1.
2.
2.
1.
3.
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1.
2.
3.
2 , 20, 2.2:
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3 , 20, 2.2:
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B. 1.
4 , 20, 2.2:
{ }ppT =
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B. 1.
5 , 20, 2.2:
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p=A,q=A ,
{ }qpqpT = ,
qp p q qp
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,
.
{ }qpqppqT = ,,
A
pq p q qp qp
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B. 2.
6 , 20, 2.2:
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1. T
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8 , 20, 2.2:
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9 , 20, 2.2:
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B. 3.
10 , 20, 2.2:
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11 , 20, 2.2:
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. 1.
12 , 20, 2.2:
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1 , ,
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1 : q . 2 r r=A, r=. 2 : , q , r A
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13 , 20, 2.2:
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1
2 $ % $ %
3 $ % $ %
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1 ...pA, qA, rA.,
pA, qA, r.
2 ,
3 ,
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14 , 20, 2.2:
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1% 1 12% 1 23% 1 34% 2 15% 2 26% 2 37% 3 18% 3 29% 3 3
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3 /
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8) 2 ( %9) 3 3 (
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15 , 20, 2.2:
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16 , 20, 2.2:
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17 , 20, 2.2:
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1. 2. 3. L
4. 5. 6. L
7. L 8. L 9. L L
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. 1
18 , 20, 2.2:
T = { p1 p2 , p1 p2 , p1 p3 } ;
1. T |= p1 (p1 p2)
2. T |= (p1 p2) p3
3. T |= (p2 p3) (p1 p3)
4. T |= (p1 p2) (p1 p3)
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. 2
19 , 20, 2.2:
1 1 2 :
1.
2. 2
3. 1 1 2
4. 1 $2 1%
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. 3
20 , 20, 2.2:
p1 p2 . ;
1. (p1 p2) (p2 p1) .
2. (p1 p2) (p1 p2) .
3. p1 p1 |= p2 p2
4. (p1 p1) p2 |= p2
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. 1
21 , 20, 2.2:
:
1 2, 2 3, , 10 1 $1 2 10% $1 2 10%
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. 2
22 , 20, 2.2:
, : .
: $ %
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. 3
23 , 20, 2.2:
,, , L,
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1. L
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6. L
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