Ringkasan logika
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RINGKASAN LOGIKA, PERKULIAHAN ILMU ALAMIAH DASAR UNIVERSITAS CIPUTRA INFERENSI DEDUKTIF LANGSUNG INFERENSI LANGSUNG OPOSISI Inverse All S is P A Some Not S is not P (L) I All S is P A Some Not S is P (S) I All S is not P E Some Not S is P (L) O All S is not P E Some Not S is not P (S) O All S is P A Some P is S I All S is not P E All P is not S E No S is P E No P is S E Some S is P I Some P is S I Obverse All S is P A No S is non-P E No S is P E All S is non-P A Some S is P I Some S is not non P O INFERENSI DEDUKTIF SILOGISME KATEGORIS Some S is not P O Some S is non P I BENTUK 1 BENTUK 2 BARBARA (AAA) CAMESTRES (AEE) Premise CELARENT (EAE) CESARE (EAE) All S is P A All Non-P is Non-S A DARII (AII) BAROKO (AOO) No S is P E Some Non-P is not non-S O FERIO (EIO) FESTINO (EIO) Some S is not P O Some Non-P is S (not non-S) O BENTUK 3 BENTUK 4 INFERENSI DEDUKSI SILOGISME HIPOTETIS DATISI (AII) CAMENES (AEE) DISAMIS (IAI) DIMARIS (IAI) FERISON (EIO) FRESISON (EIO) BOKARDO (OAO) RULES OF REPLACEMENT ~ (p ^ q) = (~p v ~q) p = ~~p ~ (p v q) = (~p ^ ~q) 6. Transposition: (p q) = (~q ~p) → → 2. Commutation: (p v q) = (q v p) 7. Material Implication: (p q) = (~p v q) → (p ^ q) = (q ^ p) 8. Material Equivalence: (p q) = [(p q) ^ (q p)} ↔ → → 3. Association: [p v (q v r)] = [(p v q) v r] (p q) = [(p ^ q) v (~p ^ ~q)} ↔ [p ^ (q ^ r)] = [(p ^ q) ^ r] 9. Exportation: [(p ^ q) r] = [p (q r)] → → → 4. Distribution: [p ^ (q v r)] = [(p ^ q) v (p ^ r)] 10. Tautology: p = (p v p) [p v (q ^ r)] = [(p v q) ^ (p v r)] p = (p ^ p) Invertend Konvertend Konverse Obvertend Kontrapositive 1. Modus Ponens (p q; p; * q) → 2. Modus Tollens (p q; ~q; * ~p) → 3. Hypothetical Syllogism (p q; q r; * p r) → → → 4. Disjunctive Syllogism (p v q; ~p; * q) 5. Constructive Dillemma (p q ^ r s; p v r; * q v s) → → Bentuk 1 = MP; SM; *SP 6. Absorption (p q; * p (p ^ q) → → Bentuk 2 = PM; SM; *SP 7. Simplification (p ^ q; * p) Bentuk 3 = MP; MS; *SP 8. Conjunction (p; q; * p ^ q) Bentuk 4 = PM; MS; *SP 9. Addition (p; * p v q) 1. De Morgan's Theorems: 5. Double Negatition:
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Transcript of Ringkasan logika
RINGKASAN LOGIKA, PERKULIAHAN ILMU ALAMIAH DASAR UNIVERSITAS CIPUTRA
INFERENSI DEDUKTIF LANGSUNG INFERENSI LANGSUNG OPOSISIInverse
All S is P A Some Not S is not P (L) IAll S is P A Some Not S is P (S) IAll S is not P E Some Not S is P (L) OAll S is not P E Some Not S is not P (S) O
All S is P A Some P is S IAll S is not P E All P is not S ENo S is P E No P is S ESome S is P I Some P is S I
ObverseAll S is P A No S is non-P ENo S is P E All S is non-P ASome S is P I Some S is not non P O INFERENSI DEDUKTIF SILOGISME KATEGORISSome S is not P O Some S is non P I BENTUK 1 BENTUK 2
BARBARA (AAA) CAMESTRES (AEE)Premise CELARENT (EAE) CESARE (EAE)
All S is P A All Non-P is Non-S A DARII (AII) BAROKO (AOO)No S is P E Some Non-P is not non-S O FERIO (EIO) FESTINO (EIO)Some S is not P O Some Non-P is S (not non-S) O
BENTUK 3 BENTUK 4INFERENSI DEDUKSI SILOGISME HIPOTETIS DATISI (AII) CAMENES (AEE)
DISAMIS (IAI) DIMARIS (IAI)FERISON (EIO) FRESISON (EIO)BOKARDO (OAO)
RULES OF REPLACEMENT~ (p ^ q) = (~p v ~q) p = ~~p~ (p v q) = (~p ^ ~q) 6. Transposition: (p q) = (~q ~p)→ →
2. Commutation: (p v q) = (q v p) 7. Material Implication: (p q) = (~p v q)→(p ^ q) = (q ^ p) 8. Material Equivalence: (p q) = [(p q) ^ (q p)}↔ → →
3. Association: [p v (q v r)] = [(p v q) v r] (p q) = [(p ^ q) v (~p ^ ~q)}↔[p ^ (q ^ r)] = [(p ^ q) ^ r] 9. Exportation: [(p ^ q) r] = [p (q r)]→ → →
4. Distribution: [p ^ (q v r)] = [(p ^ q) v (p ^ r)] 10. Tautology: p = (p v p)[p v (q ^ r)] = [(p v q) ^ (p v r)] p = (p ^ p)
Invertend
Konvertend Konverse
Obvertend
Kontrapositive
1. Modus Ponens (p q; p; * q)→2. Modus Tollens (p q; ~q; * ~p)→3. Hypothetical Syllogism (p q; q r; * p r)→ → →4. Disjunctive Syllogism (p v q; ~p; * q)5. Constructive Dillemma (p q ^ r s; p v r; * q v s)→ → Bentuk 1 = MP; SM; *SP6. Absorption (p q; * p (p ^ q)→ → Bentuk 2 = PM; SM; *SP7. Simplification (p ^ q; * p) Bentuk 3 = MP; MS; *SP8. Conjunction (p; q; * p ^ q) Bentuk 4 = PM; MS; *SP9. Addition (p; * p v q)
1. De Morgan's Theorems: 5. Double Negatition:
