Artificial Intelligence: Knowledge Representation And Reasoning Week 8 Answer
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AI Knowledge Representation And Reasoning Week 8 Answer (Jan-Apr 2025)
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1. Which of the following can be defined as a symmetric relation?
a) Bombed(X,Y)
b) Brother(X,Y)
c) Citizen(X,Y)
d) Classmate(X,Y)
e) ParallelTo(X,Y)
f) Parent(X,Y)
g) Prefix(X,Y)
h) PrimeFactor(X,Y)
2. Which of the following can be defined as an antisymmetric relation?
a) Bombed(X,Y)
b) Brother(X,Y)
c) Citizen(X,Y)
d) Classmate(X,Y)
e) ParallelTo(X,Y)
f) Parent(X,Y)
g) Prefix(X,Y)
h) PrimeFactor(X,Y)
3. Which of the following can be defined as an asymmetric relation?
a) Bombed(X,Y)
b) Brother(X,Y)
c) Citizen(X,Y)
d) Classmate(X,Y)
e) ParallelTo(X,Y)
f) Parent(X,Y)
g) Prefix(X,Y)
h) PrimeFactor(X,Y)
4. Which of the following can be defined as a transitive relation?
a) Bombed(X,Y)
b) Brother(X,Y)
c) Citizen(X,Y)
d) Classmate(X,Y)
e) ParallelTo(X,Y)
f) Parent(X,Y)
g) Prefix(X,Y)
h) PrimeFactor(X,Y)
5. Can we consider every asymmetric relation to be antisymmetric as well?
a) Yes
b) No
6. Is the given FOL formula valid?
(∀x∀y[R(x,y) ⊃ ¬R(y,x)]) ⊃ (∀u∀v[(R(u,v) ∧ R(v,u)) ⊃ (u=v)])
(Hint: the term “valid” has a well-defined meaning in FOL.)
(Hint: use the Resolution Refutation Method to prove/disprove validity of the formula.)
a) Valid
b) Invalid
c) Cannot be proved/disproved by using Resolution Refutation Method
AI Knowledge Representation And Reasoning Week 8 Answer
7. Determine the truth value of the formula when the domain of interest is empty, i.e., when there are no elements in the domain.
(∀x P(x)) ⊃ (∃y P(y))
a) True
b) False
c) Cannot be determined because the meaning of P(x) is not known.
8. Express the statement “books are disjoint from men and women” in FOL.
a) ∀x { Book(x) ⊃ ￢[ Man(x) ∨ Woman(x) ] }
b) ∀x { Book(x) ⊃ ￢[ Man(x) ∧ Woman(x) ] }
c) { ∀x [ Book(x) ⊃ ￢Man(x) ] } ∨ { ∀y [ Book(y) ⊃ ￢Woman(y) ] }
d) { ∀x [ Book(x) ⊃ ￢Man(x) ] } ∧ { ∀y [ Book(y) ⊃ ￢Woman(y) ] }
9. Express the statement “those who like a book have read that book” in FOL.
a) ∀x∀y { Likes(x,y) ∧ Book(y) ∧ Read(x,y) }
b) ∀x∀y { [ Likes(x,y) ∧ Book(y) ] ⊃ Read(x,y) }
c) ∀x∀y { Likes(x,y) ⊃ [ Book(y) ⊃ Read(x,y) ] }
d) ∃x∃y { Likes(x,y) ∧ Book(y) ∧ Read(x,y) }
10. Only people read books.
a) ∀x∀y { [ Person(x) ∧ Read(x,y) ] ⊃ Book(y) }
b) ∀x∀y { [ Read(x,y) ∧ Book(y) ] ⊃ Person(x) }
11. There exists a book no one likes.
a) ∃y { Book(y) ∧ [ ∀x ￢Likes(x,y) ] }
b) ∃y∀x { Book(y) ⊃ ￢Likes(x,y) }
12. Provide a FOL definition for P(x) that represents men who have read some book.
a) ∀x∀y { P(x) ≡ [ Man(x) ∧ Read(x,y) ∧ Book(y) ] }
b) ∀x { P(x) ≡ [ Man(x) ∧ ∃y ( Read(x,y) ∧ Book(y) ) ] }
c) ∀x { P(x) ≡ ∃y [ Man(x) ∧ Read(x,y) ∧ Book(y) ] }
d) ∀x∃y { P(x) ≡ [ Man(x) ∧ Read(x,y) ∧ Book(y) ] }
13. A triple in RDF/RDFS document is ____________.
a) An edge in a semantic graph
b) Not capable of expressing subclass relationship between two classes
c) Capable of expressing subproperty relationship between two properties
d) Capable of expressing membership in a class
14. A property in an RDF/RDFS data model ____________.
a) Represents a binary relation
b) Is a resource
c) Links a resource to another resource
d) Represents an undirected edge in a semantic graph
15. How many triples are written in this RDF document? (Ignoring @prefix definitions.)
16. When you treat the above RDF document as a KB, what can be inferred from it?
a) :Ada rdf:type :Woman.
b) :Ada :parent :Bob.
c) :Man rdf:type rdfs:Class.
d) :Ron rdf:type :Man.
Nptel AI Knowledge Representation And Reasoning Week 8 Answer (Jan-Apr 2025)
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