Fundamentals of Artificial Intelligence Week 5 Answers
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Fundamentals of Artificial Intelligence Week 5 Answers (July-Dec 2025)
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Question 1. In First Order Logic, the elements of a conceptualization include ______
A) universe of discourse and an interpretation.
B) well-formed expression.
C) objects, relations and functions.
D) meaningful expression.
Question 2. P, Q and R are logical propositions. Identify the statements as tautology, and/or contradiction?
I. ((P∨Q)∧R)↔((P∧R)∨(Q∧R))( (P ∨ Q) ∧ R ) ↔ ( (P ∧ R) ∨ (Q ∧ R) )((P∨Q)∧R)↔((P∧R)∨(Q∧R))
II. (P↔Q)∧(Q↔R)∧¬(P↔R)(P ↔ Q) ∧ (Q ↔ R) ∧ ¬(P ↔ R)(P↔Q)∧(Q↔R)∧¬(P↔R)
A) I. Tautology; II. Contradiction.
B) I. Contradiction; II. Tautology.
C) Both Tautologies.
D) Both Contradictions.
Question 3. Facts and rules that attempt to capture all of the (important) facts and concepts about a domain are referred to as ______
A) definitions.
B) axioms.
C) theorems.
D) truth values.
These are Fundamentals of Artificial Intelligence Week 5 Answers
Question 4. Skolemization is a procedure for systematic elimination of the ______ in a first-order formula in a prenex form, by introducing new constant and functional symbols.
A) existential quantifiers
B) universal quantifiers
C) variable
D) function
Question 5. An axiom is a well-formed formula that is asserted to be true without proof. In an AI system, the axioms would be:
A) The domain-specific knowledge rules in the database.
B) The control strategy rules selected by the inference mechanism.
C) The input data supplied by the user.
D) The output data obtained through the inference process.
Question 6. A sentence in a formal language is true if and only if it accurately describes the world according to our conceptualization. ______ is a mapping between elements of the language and elements of a conceptualization.
A) Declarative semantics.
B) An interpretation.
C) A representation.
D) An assignment.
Question 7. Assertion A: Any predicate calculus well-formed formula can be converted to a set of clauses.
Reason R: The prenex form consists of a string of quantifiers called prefix followed by a quantifier-free formula called the matrix.
A) Both A and R are true and R is the correct explanation for A.
B) Both A and R are true but R is not the correct explanation for A.
C) A is True but R is False.
D) A is false but R is True.
These are Fundamentals of Artificial Intelligence Week 5 Answers
Question 8. Consider the predicate Likes(x,y): x likes y.
Everyone likes ice cream. Is it possible to convey the same meaning using an existential statement? If yes, give the existential statement.
A) No.
B) Yes. ∀x Likes(x, Icecream)
C) Yes. ∃x Likes(x, Icecream)
D) Yes. ¬ ∃x ¬ Likes(x, Icecream)
Question 9. Write the FOL formula obtained by introducing the skolem function Support(x) in the NEXT step towards arriving at the Clausal Normal Form for the following: ∀x[¬Brick(x)∨(∃y[On(x,y)∧¬Pyramid(y)]∧∀y[¬On(x,y)∨¬On(y,x)])]∀x\bigl[¬Brick(x) \lor ( ∃y[On(x,y) ∧ ¬Pyramid(y)] ∧ ∀y[¬On(x,y) ∨ ¬On(y,x)])\bigr]∀x[¬Brick(x)∨(∃y[On(x,y)∧¬Pyramid(y)]∧∀y[¬On(x,y)∨¬On(y,x)])]
A) ∀x[¬Brick(x) ∨ ([On(x, Support(x)) ∧ ¬Pyramid(y)] ∧ ∀y[¬On(x,y) ∨ ¬On(y,x)])]
B) ∀x[¬Brick(x) ∨ (∃y[On(x, Support(x)) ∧ ¬Pyramid(Support(x))] ∧ ∀y[¬On(x,y) ∨ ¬On(y,x)])]
C) ∀x[¬Brick(x) ∨ ([On(x, Support(x)) ∧ ¬Pyramid(Support(x))] ∧ ∀y[¬On(x,y) ∨ ¬On(y,x)])]
D) ∀x[¬Brick(x) ∨ ([On(x, Support(x)) ∧ ¬Pyramid(Support(x))] ∧ [¬On(x, Support(x)) ∨ ¬On(Support(x), x)])]
Question 10. A definition of a predicate is a biconditional, and can be decomposed into a necessary and sufficient descriptions. Which of the following statement are true with regards to definition of `Brother’?
I. Being Male’ is a necessary condition for being a Brother’, but it is not sufficient.
II. Being a Male’ Sibling’ is a necessary and sufficient condition for being a `Brother’.
A) I Only
B) II Only
C) Both I and II
D) None
These are Fundamentals of Artificial Intelligence Week 5 Answers