1. MATERI III
PROPOSISI

2. Rules of Inference

3. Proofs - A little proof…
Here’s what you know:
Ellen is a math major or a CS major.
If Ellen does not like discrete math, she is not a CS major.
If Ellen likes discrete math, she is smart.
Ellen is not a math major.
Can you conclude Ellen is smart?
M  C
D  C
D  S M

4. Proofs - A little proof…
M  C Given
D  C Given
D  S Given
M Given
C Elimination (1,4)
C  D Contrapositive of 2
C  S Transitivity (6,3)
S Modus Ponens (5,7)
Then, we conclude that Ellen is smart.

5. ALJABAR PROPOSISI Idempoten p v p ≡ p p ᴧ p ≡ p
Asosiatif (p ᴧ q) ᴧ r ≡ p ᴧ (q ᴧ r)
(p v q) v r ≡ p v (q v r)
Komutatif p v q ≡ q v p
p ᴧ q ≡ q ᴧ p
Distributif p ᴧ (q v r) ≡ (p ᴧ q) v (p ᴧ r)
p v (q ᴧ r) ≡ (p v q) ᴧ (p v r)

6. ALJABAR PROPOSISI Identitas p v f ≡ p p v t ≡ t p ᴧ f ≡ f p ᴧ t ≡ p
Komplemen ̴t ≡ f ̴f ≡ t
p v ̴p ≡ t p ᴧ ̴p ≡ f
Involution ̴( ̴p) ≡ p
De Morgan’s ̴(p ᴧ q) ≡ ̴p v ̴q
̴(p v q) ≡ ̴p ᴧ ̴q

7. ALJABAR PROPOSISI Absorpsi p v (p ᴧ q) ≡ p p ᴧ (p v q) ≡ p
Implikasi p → q ≡ ̴p v q
Biimplikasi p ↔ q ≡ (p → q)ᴧ(q → p)
Kontraposisi p → q ≡ ̴ q → ̴ p

8. Exercises
Use truth tables to determine whether the following argument forms are valid.

9. Exercises
Use truth tables to determine whether the following argument forms are valid.
Jika sistem digital maka akurat dan jika gerbang logika maka aljabar Boole.
Sistem digital atau gerbang logika
Tidak akurat atau bukan aljabar Boole
Akurat
Δ Sistem digital

10. Exercises
Simplify using proposition algebra (p ᴧ ̴ (p v ̴ q)) v p ᴧ (p v q) ((p v q) ᴧ ̴ p) v ̴ (p v q) v ( ̴ p ᴧ q) ( ̴ p ᴧ (q → ̴ r)) v ((p v r) ↔ q )