CS362 Intelligent Systems
Dr. Elshaimaa Nada
Assignment No.1
1. Translate the following English sentences into first-order logic formulas, and
vice versa.
a) Some students take ADB
……………………………………………..
b) Every student who takes ADB passes it
…………………………………………..
c) No good student flunks an exam
……………………………………………..
d) Brothers are siblings (express the fact that “sibling” is a symmetric relation)
……………………………………………..
e) …………………………………………….
friends(harry,potter) ^ friends(potter , harry)
f)
One’s mother is one’s female parent
……………………………………………..
g) ………………………………………………………
XY(cousin (X,Y)  →N M( parent_of (M,Y) ^ sibling (N,M) ^ parent_of (N,X)
^ ¬ (N=M)))
h) ………………………………………………………
XY Z (mother_of (X,Z) ^ mother_of(Y,Z) → X = Y)
i)
If it isn’t cloudy tomorrow, Harry will go to the zoo and will not take his umbrella
with him.
……………………………………………..
j)
………………………………………………..
X ( (bird(X) ^ crow (X) ) ^ ¬ Z ( birds(Z) ^ squirrel (Z))
k) If one or more lives are lost then all lives are lost

2. Translate the following formulas into natural English, and vice versa.
a) X(male(X) V female(X))
……………………………………………..
b) X ((father(X) → male(X)) ^ (mother(X) → female(X)))
……………………………………………..
c) ……………………………………………..
No one can be both a father and a mother
3. A new operator,
, or exclusive-or, may be defined by the following truth table:
P
Q
T
T
F
T
F
T
F
T
T
F
F
F
P
Q
Create a propositional calculus expression using only ^, V and ¬ that is
equivalent to P
P
Q
T
T
F
F
T
F
T
F
P
F
T
T
F
Q. Prove their equivalence using truth tables.
Q
¬P
¬Q
P ^ ¬Q
(P
¬P ^ Q Equivalence
Q) =
CS362 Intelligent Systems
Dr. Elshaimaa Nada
4. Attempt to unify the following pairs of expressions. Either show their most
general unifiers or explain why they will not unify.
a) p(X,Y) and p(a,Z)
……………………………………………..
b) p(X,X) and p(a,b)
……………………………………………..
c) ancestor(X,Y) and ancestor(bill, father(bill))
……………………………………………..
d) q(X) and ¬q(a)
……………………………………………..