COS2661 Assignment 3 2024 solutions
COS2661 Assignment 3 2024 solutions
QUESTION 1 In this question you have to translate sentences of English
sentences into First-Order Logic, using the predicates and names given
in Table 1
1.1 Nothing to the left of Tabiso is larger than everything to the left of
Tafara.
¬∃x (LeftOf(x, Tabiso) ∧ ∀y (LeftOf(y, Tafara) → Larger(x, y)))
1.2 Anything to the left of Tabiso is smaller than something that is in
back of every pet to the
right of Tafara.
∀x (LeftOf(x, Tabiso) → ∃y (Pet(y) ∧ RightOf(Tafara, y) ∧ BackOf(y, z) ∧ Smaller(x, z)))
1.3Every student gave a pet to some other student sometime or other.
∀x (Student(x) → ∃y ∃z (Student(y) ∧ Pet(z) ∧ x ≠ y ∧ Gave(x, z, y)))
1.4No student fed every pet.
¬∃x (Student(x) ∧ ∀y (Pet(y) → Fed(x, y)))
1.5If Tabiso ever gave Tafara a pet, she owned it then, and he didn’t.
∃z (Pet(z) ∧ Gave(Tabiso, z, Tafara) → (Own(Tafara, z) ∧ ¬Own(Tabiso, z)))
COS2661 Assignment 3 2024 solutions
QUESTION 1 In this question you have to translate sentences of English
sentences into First-Order Logic, using the predicates and names given
in Table 1
1.1 Nothing to the left of Tabiso is larger than everything to the left of
Tafara.
¬∃x (LeftOf(x, Tabiso) ∧ ∀y (LeftOf(y, Tafara) → Larger(x, y)))
1.2 Anything to the left of Tabiso is smaller than something that is in
back of every pet to the
right of Tafara.
∀x (LeftOf(x, Tabiso) → ∃y (Pet(y) ∧ RightOf(Tafara, y) ∧ BackOf(y, z) ∧ Smaller(x, z)))
1.3Every student gave a pet to some other student sometime or other.
∀x (Student(x) → ∃y ∃z (Student(y) ∧ Pet(z) ∧ x ≠ y ∧ Gave(x, z, y)))
1.4No student fed every pet.
¬∃x (Student(x) ∧ ∀y (Pet(y) → Fed(x, y)))
1.5If Tabiso ever gave Tafara a pet, she owned it then, and he didn’t.
∃z (Pet(z) ∧ Gave(Tabiso, z, Tafara) → (Own(Tafara, z) ∧ ¬Own(Tabiso, z)))
