4. symbolic logic

20
Deductive Logic (Symbolic/ Modern)

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Page 1: 4. symbolic logic

Deductive Logic (Symbolic/ Modern)

Page 2: 4. symbolic logic

4 August 1834 – 4 April 1923

A B

A B

AB

A ^ B = Ø

A ^ B ≠ Ø

A subset BA subset BA subset B

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The Rule of Replacement

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Rule of Replacement

01. De Morgan's Theorems02. Commutation03. Association04. Distribution05. Double Negation06. Transposition07. Material Implication08. Material Equivalence09. Exportation10. Tautology

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De Morgan's Theorm

~(p ^ q) = ~p or ~q

~(p v q) = ~p and ~q

Page 6: 4. symbolic logic

Commutation

(p or q) = (q or p)

(p and q) = (q and p)

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Association

[p or (q or r)] = [(p or q) or r]

[p and (q and r)] = [(p and q) and r]

Page 8: 4. symbolic logic

Distribution

[p and (q or r) = [(p and q) or (p and r)]

[p or (q and r)] = [(p or q) and (p or r)]

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Double Negation

p = ~~p

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Transposition

(if p > q) = (if ~q > ~p)

Jika nilai ujian saya lebih dari 60 maka saya lulus =

Jika saya tidak lulus maka nilai ujian saya tidak lebih dari 60

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Material Implication

(jika p maka q) = (~p or q)

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Material Equivalence

(If only if p > q) = [(if p > q) and (if q > p)]

(If only if p > q) = [(p and q) or (~p and ~q)]

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Exportation

[if (p and q) > r] = [if p > (if q > r)]

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Tautology

p = (p or p)

p = (p and p)

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Truth Table

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Material Nonimplication(Material Implication)

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Latihan

Tunjukkan apakah argumen berikut valid atau tidak valid:

(a → b) ^ [(a ^ b) → c]

a → (c → d)

--------------------

a → d

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Latihan

Tunjukkan apakah preposisi berikut setara?

a → (b → c) = (a → b) → c

Page 19: 4. symbolic logic

Latihan

Tunjukkan, valid atau tidak argumen berikut:

JIKA konsumsi bensin meningkat, MAKA impor bensin meningkat DAN subsidi pemerintah terhadap bensin meningkat.

JIKA impor bensin meningkat ATAU subsidi pemerintah terhadap bensin meningkat, maka keuangan negara akan defisit.

KARENA ITU, jika konsumsi bensin terus meningkat, maka keuangan negara akan defisit.

Page 20: 4. symbolic logic