[MATERI] Aturan Penyimpulan dan Aturan Penggantian

ATURAN PENYIMPULAN

1. Modus Ponens (MP)

p → q

p / ∴ q

2. Modus Tolens (MT)

p → q

~q / ∴ p

3. Hypothetical Syllogisme (HS)

p → q

q → r / ∴ p → r

4. Disjunctive Syllogisme (DS)

p v q

~ p / ∴ q

5. Constructive Dillema (CD)

( p → q ) ∧ ( r → s )

p v r / ∴ q v s

6. Destructive Dillema (DD)

( p → q ) ∧ ( r → s )

~ q v ~ s / ∴ ~p v ~r

7. Conjunction (Conj)

p

q / ∴ p ∧ q

8. Simplification (Simpl)

p ∧ q

∴ p

9. Addition ( Add)

p

∴ p v q


ATURAN PENGGANTIAN

1. De Morgan

a. ~ ( p ∧ q ) ≡ ~ p v ~ q

b. ~ ( p v q ) ≡ ~ p ∧ ~ q

2. Komutatif

a. ( p ∧ q ) ≡ ( q ∧ p )

b. ( p v q ) ≡ ( q v p )

3. Asosiatif

a. ( p v q ) v r ≡ p v ( q v r )

b. ( p ∧ q ) ∧ r ≡ p ∧ ( q ∧ r )

4. Distributif

a. ( p v q ) ∧ r ≡ ( p ∧ r ) v ( q ∧ r )

b. ( p ∧ q ) v r ≡ ( p v r ) ∧ ( q v r )

5. Dobel Negasi

~ ( ~ p ) ≡ p

6. Implikasi

p → q ≡ ~ p v q

7. Material Equivalen

a. p ∧ q ≡ ( p → q ) ∧ ( q → p )

b. p ∧ q ≡ ( p ∧ q ) v ( ~ p ∧ ~ q )

8. Eksportasi

p → ( q → r ) ≡ ( p ∧ q ) → r

9. Transposisi

p → q ≡ ~ q → ~ p

10. Tautologi

a. ( p v p ) ≡ p

b. ( p ∧ p ) ≡ p