CSE630 Homework 3
Jason Kim

1.
1- P->Q (If P is true, then Q must be true for the statement to be true)
2- ~P /\ ~Q  (If P is false, then ~P is True, for the statement to be true, Q cannot be True)
3- P V Q (Either P or Q is true for this statement to be true)
4- (P /\ Q) V M (P and Q are True, and M is false, the OR symbol must be used to make the statement true)
5- John(P) /\ Peter(Q)
P = Tall
Q = Short Hair

2. 
1- (~Q /\ S ) goes to ~Q (Specialization rule), Given ~Q, then P->Q gives ~P by Modus Tollens.  
2-(~Q /\ T ) goes to ~Q (Specialization rule), Given ~Q, then S->Q gives ~P by Modus Tollens.  
3-S /\ ~W goes to ~W or S (Specialization rule)
4- R->W given R gives W (Modus Ponens) or given ~W gives ~R (Modus Tollens)
5-P V R gives P or R by Generalization rule, given ~P gives R or given ~R gives P by Elimination rule
a. ~W /\ ~Q becomes ~(W V Q) by De Morgans Law
b. ~(Q /\ S) becomes ~Q V ~S by De Morgans Law

3. 
1-FastRunners(Lori)
2-RoaringAnimals(Lions)
3- E (There Exists):x Frog(x) /\ In(x,BuckeyeCreek) 



4. Only 1 thing in the KB, since a KB is a set of sentences.


5.
8.6
a E:x Student(x) /\ TookFrench(x,Spring2001); Definition: TookFrench( Student, Quarter)  A Student Took French in Quarter
b V x Student(x) /\ PassesClass(x,French); Definition: PassesClass(Student,Class) A Student Passes a Class
c E x GreekClass(x) /\ OnlyHasOneStudent(x,Spring2001); Definition: OnlyHasOneStudent(Class,Quarter) A Class only has one student in Quarter
d V x BestScore(x) /\ Greek(x) > French(x) ; Definition Bestscore is the best score of a respective Class
e V x PeopleWhoBuyPolicy(x) /\ IsSmartPerson(x) ; PeoplewhobuyPolicy buys policys, IsSmartPerson is a smart perosn 
h E x,y Barber(x),MenWhoDontShaveThemselves(y) /\ Shave(x,y) ; Menwhodontshavethemselves is men who dont shave themselves
i V x PersonBorninUK(x) /\ ParentisUKCitizen(x) -> IsUKCitizen(x) ;  PersonborninUK is someone borin in UK, ParentisUKCitizen is their parent is a citizen, IsUKcitizen means they are a UK citizen


6. IsMarried(Female,Spouse)


7.a.
Axioms
V x STENCH(x) /\ WUMPUS(x)
V x BREEZE(x) /\ PIT(x)
V x GLITTER(x) /\ GOLD(x)

Facts
ASK(KB,BREEZE(x,y))
ASK(KB,STENCH(x,y))
ASK(KB,GLITTER(x,y))
ASK(KB,GOLD(x,y))
ASK(KB,ARCHER(x,y))
ASK(KB,WUMPUS(x,y))
ASK(KB,PIT(x,y))