NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 8 Assignment Answers 2025
1. Which of the following can be defined as a symmetric relation?
- Bombed(X,Y)
- Brother(X,Y)
- Citizen(X,Y)
- Classmate(X,Y)
- ParallelTo(X,Y)
- Parent(X,Y)
- Prefix(X,Y)
- PrimeFactor(X,Y)
Answer :- For Answers Click Here
2. Which of the following can be defined as an antisymmetric relation?
- Bombed(X,Y)
- Brother(X,Y)
- Citizen(X,Y)
- Classmate(X,Y)
- ParallelTo(X,Y)
- Parent(X,Y)
- Prefix(X,Y)
- PrimeFactor(X,Y)
Answer :-
3. Which of the following can be defined as an asymmetric relation?
- Bombed(X,Y)
- Brother(X,Y)
- Citizen(X,Y)
- Classmate(X,Y)
- ParallelTo(X,Y)
- Parent(X,Y)
- Prefix(X,Y)
- PrimeFactor(X,Y)
Answer :-
4. Which of the following can be defined as a transitive relation?
- Bombed(X,Y)
- Brother(X,Y)
- Citizen(X,Y)
- Classmate(X,Y)
- ParallelTo(X,Y)
- Parent(X,Y)
- Prefix(X,Y)
- PrimeFactor(X,Y)
Answer :-
5. Can we consider every asymmetric relation to be antisymmetric as well?
- Yes
- No
Answer :-
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.)
- Valid
- Invalid
- Cannot be proved/disproved by using Resolution Refutation Method
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))
- True
- False
- Cannot be determined because the meaning of P(x) is not known.
Answer :-
END GROUP 1
BEGIN GROUP 2
Consider L(P,F,C) where
P: { Man(m), Woman(w), Person(p), Book(b), Likes(x,y), Read(x,y) }
F: { pageCount(x) }
C: { Ada, Ben, FOL, DL, Prolog, KRR }
where, Likes(x,y) means “x likes y”; Read(x,y) means “x read y”; we use “people” and “person” interchangeably.
Use models (and those that are not models) to unpack the meaning of FOL formulas.
8. Express the statement “books are disjoint from men and women” in FOL.
- ∀x { Book(x) ⊃ ￢[ Man(x) ∨ Woman(x) ] }
- ∀x { Book(x) ⊃ ￢[ Man(x) ∧ Woman(x) ] }
- { ∀x [ Book(x) ⊃ ￢Man(x) ] } ∨ { ∀y [ Book(y) ⊃ ￢Woman(y) ] }
- { ∀x [ Book(x) ⊃ ￢Man(x) ] } ∧ { ∀y [ Book(y) ⊃ ￢Woman(y) ] }
Answer :-
9. Express the statement “those who like a book have read that book” in FOL.
- ∀x∀y { Likes(x,y) ∧ Book(y) ∧ Read(x,y) }
- ∀x∀y { [ Likes(x,y) ∧ Book(y) ] ⊃ Read(x,y) }
- ∀x∀y { Likes(x,y) ⊃ [ Book(y) ⊃ Read(x,y) ] }
- ∃x∃y { Likes(x,y) ∧ Book(y) ∧ Read(x,y) }
Answer :-
10. Only people read books.
- ∀x∀y { [ Person(x) ∧ Read(x,y) ] ⊃ Book(y) }
- ∀x∀y { [ Read(x,y) ∧ Book(y) ] ⊃ Person(x) }
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11. There exists a book no one likes.
- ∃y { Book(y) ∧ [ ∀x ￢Likes(x,y) ] }
- ∃y∀x { Book(y) ⊃ ￢Likes(x,y) }
Answer :-
12. Provide a FOL definition for P(x) that represents men who have read some book.
- ∀x∀y { P(x) ≡ [ Man(x) ∧ Read(x,y) ∧ Book(y) ] }
- ∀x { P(x) ≡ [ Man(x) ∧ ∃y ( Read(x,y) ∧ Book(y) ) ] }
- ∀x { P(x) ≡ ∃y [ Man(x) ∧ Read(x,y) ∧ Book(y) ] }
- ∀x∃y { P(x) ≡ [ Man(x) ∧ Read(x,y) ∧ Book(y) ] }
Answer :-
13. A triple in RDF/RDFS document is _____________ .
- an edge in a semantic graph
- not capable of expressing subclass relationship between two classes
- capable of expressing subproperty relationship between two properties
- capable of expressing membership in a class
Answer :-
14. A property in a RDF/RDFS data model _________________ .
- represents a binary relation
- is a resource
- links a resource to another resource
- represents an undirected edge in a semantic graph
Answer :-
15. An RDF/RDFS document in Turtle format is given below. Note: RDF document is case sensitive, so pay attention to lower/upper case.
@prefix : http://nptel.iitm.ac.in/krr/tutorial/
@prefix rdf: http://www.w3.org/1999/02/22-rdf-syntax-ns#
@prefix rdfs: http://www.w3.org/2000/01/rdf-schema#
:Book rdf:type rdfs:Class.
:Person rdf:type rdfs:Class.
:Man rdfs:subClassOf :Person.
:Woman rdfs:subClassOf :Person.
:parent rdf:type rdf:Property.
:mother rdfs:subPropertyOf :parent.
:father rdfs:subPropertyOf :parent.
:Ada :mother :Bob.
:Ron :father :Bob
How many triples are written in this RDF document? Ignore @prefix definitions.
Answer :-
16. When you treat the above RDF document as a KB then what can be inferred from it?
- :Ada rdf:type :Woman.
- :Ada :parent :Bob.
- :Man rdf:type rdfs:Class.
- :Ron rdf:type :Man.
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