Exercise 1

Artifical Intelligence Excercise 1
1. Semantic Network
2. Semantice Network
3. Truth Tables
a) ɿ(ɿP) = P
P ɿP ɿ (ɿP)
T
F
T
F
F
T
F
T
T
F
T
F
Has
Property
Has
Property
Has
Property
Is - a
Is - a
Has
Property
Is - a
Has
Color
Has
Property
Has
Covering
Is - a
White
Singing
Tweety
Canary
FlyingBirdFeatherd
Animal
Equilateral
Triangle
Triangle
Closed Shape
3 Angles 3 Sides
Equal Slides

B) (P v Q) Ξ (ɿP → Q)
C) (P → Q) Ξ (ɿQ → ɿP)
D) (i) ɿ (P v Q) Ξ (ɿP ^ ɿQ)
(ii) ɿ (P ^ Q) Ξ (ɿP v ɿQ)
P Q P v Q ɿP ɿP → Q
T
F
T
F
T
T
F
F
T
T
T
F
F
T
F
T
T
T
T
F
P Q ɿQ ɿP P → Q ɿQ → ɿP
T
F
T
F
T
T
F
F
F
F
T
T
F
T
F
T
T
T
F
T
T
T
F
T
P Q ɿQ ɿP P v Q ɿ (P v Q) ɿP ^ ɿQ
T
F
T
F
T
T
F
F
F
F
T
T
F
T
F
T
T
T
T
F
F
F
F
T
F
F
F
T
P Q ɿQ ɿP P ^ Q ɿ (P ^ Q) ɿP v ɿQ
T
F
T
F
T
T
F
F
F
F
T
T
F
T
F
T
T
F
F
F
F
T
T
T
F
T
T
T

e) i) (P v Q) Ξ (Q v P)
ii) (P ^ Q) Ξ (Q ^ P)
f) (P ^ Q) ^ R Ξ P ^ (Q ^ R)
P Q P v Q Q v P
T
F
T
F
T
T
F
F
T
T
T
F
T
T
T
F
P Q P ^ Q Q ^ P
T
F
T
F
T
T
F
F
T
F
F
F
T
F
F
F
P Q R P ^ Q (Q ^ R) (P ^ Q) ^ R P ^ (Q ^ R)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
T
F
F
F
F
F
F
T
F
F
F
T
F
F
F
T
F
F
F
F
F
F
F
T
F
F
F
F
F
F
F

g) (P v Q) v R Ξ P v (Q v R)
h) P v (Q ^ R) Ξ (P v Q) ^ (P v R)
P Q R P v Q Q v R (P v Q) v R P v (Q v R)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
T
T
T
T
T
F
F
T
T
T
T
T
T
T
F
T
T
T
F
T
T
T
F
T
T
T
T
T
T
T
F
P Q R Q ^ R P v Q P v R P v (Q ^ R) (P v Q) ^ (P v R)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
F
F
F
T
F
F
F
T
T
T
T
T
T
F
F
T
T
T
T
T
F
T
F
T
T
T
T
T
F
T
F
T
T
T
T
T
F
T
F

i) P ^ (Q v R) Ξ (P ^ Q) v (P ^ R)
4. Truth Tables
i) (p ^ (p → q)) → q
ii) (p → q) ^ ɿq → ɿq
P Q R Q v R P ^ Q P ^ R P ^ (Q v R) (P ^ Q) v (P ^ R)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
T
T
F
T
T
T
F
T
T
F
F
F
F
F
F
T
F
T
F
F
F
F
F
T
T
T
F
F
F
F
F
T
T
T
F
F
F
F
F
p q p → q p ^ (p → q) (p ^ (p → q)) → q
T
F
T
F
T
T
F
F
T
T
F
T
T
F
F
F
T
T
T
T
P q p → q ɿq (p → q) ^ ɿq (p → q) ^ ɿq → ɿq
T
F
T
F
T
T
F
F
T
T
F
T
F
F
T
T
F
F
T
T
T
T
T
T

iii) (P → (Q → R)) → (P → Q)) → (P → R)
5.
(P → Q) ^ (Q → P) Ξ P ↔ Q
P Q R Q → R P → Q P → R P → (Q →
R)
P → (Q →
R)→ (P →
Q))
P → (Q →
R)→ (P →
Q))→ (P →
R)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
F
T
T
T
F
T
T
T
T
F
F
T
T
T
T
T
F
T
F
T
T
T
T
T
F
T
T
T
T
T
T
T
F
T
T
T
T
T
T
T
T
T
T
T
T
T
T
P Q P → Q Q → P (p → q) ^
Q → P
P ↔ Q
T
F
T
F
T
T
F
F
T
T
F
T
T
F
T
T
T
F
F
T
T
F
F
T

Exercise 1

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