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									                                         Tutorial 7
Q1: For each pair of atomic sentences, give the most general unifier if it exists:

    1.   P(A,B,B) and P(x,y,z)
    2.   Q(y,G(A,B)) and Q(G(x,x),y)
    3.   Older(Father(y),y) and older(Father(x),Ali)
    4.   Knowx(Father(y),y) and Knows(x,x)

Q2: Write down logical representations for the following sentences suitable for use with
GMP
   1. Horses, cows and pigs are mammals.
   2. An offspring of a horse is a horse.
   3. Bluebeard is a horse.
   4. Bluebeard is Charlie’s parent.
   5. Offspring and parent are inverse relations.
   6. Every mammal has a parent.

Q3: Here are two sentences in the language of first order language.
   1. (A):
    2. (B):
   Assume that the variables range over all the natural numbers 0,1,2,.......,∞ and that the “
    “≥” means “is greater or equal to”. Under this interpretation, translate (A) and (B) into
    English (and Arabic).
   Is (A) true under this interpretation?
   Is (B) true under this interpretation?
   Does (A) entail (B)?
   Does (B) entail (A)?

								
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