NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 2 Assignment Answers 2025

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NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 2 Assignment Answers 2025

1. A sentence in logic is a statement that in principle has a truth value. Which of the following are sentences in logic?

  • Did Joe pardon his son?
  • Joe said he will not pardon his son.
  • Joe did not pardon his son.
  • Please sign a law banning voter ID.
  • Governor signed a law banning voter ID.
Answer :- For Answers Click Here

2. Select the reasoning method(s) that lead to logically sound arguments

  • Abduction
  • Deduction
  • Both of the above
  • None of the above
Answer :-

3. Select the formulas that are tautologies.

  • P ⊃ (¬P ⊃ P)
  • (P ⊃ P) ⊃ ¬P
  • ¬P ⊃ (P ⊃ P)
  • (P ⊃ Q) ∨ (Q ⊃ R)
Answer :-

4. Given three formulas P, Q and R, a rule of inference such as {P, Q} ⊢ R is said to be valid if and only if ________________ .

  • ((P ∧ Q) ⊃ R) is satisfiable
  • ((P ∧ Q) ⊃ R) is a tautology
  • (¬P ∨ ¬Q ∨ R) is satisfiable
  • (¬P ∨ ¬Q ∨ R) is a tautology
  • (P ∧ Q ∧ ¬R) is satisfiable
  • (P ∧ Q ∧ ¬R) is a tautology
Answer :-

5. Select the valid rules of substitution.

  • [¬(P ⊃ Q)] ≡ [¬P ⊃ ¬Q]
  • [P ⊃ Q] ≡ [¬Q ⊃ ¬P]
  • [¬P ⊃ ¬Q] ≡ [P ∨ ¬Q]
  • [P ⊃ R] ⊃ [(P ∧ Q) ⊃ R]
Answer :-

6. Select the valid rules of inference.

  • {P ⊃ Q, P} ⊢ Q
  • {P ⊃ Q, ¬P} ⊢ ¬Q
  • {P ∧ Q} ⊢ (P ∨ Q)
  • {P ⊃ R} ⊢ ((P ∧ Q) ⊃ R)
Answer :- For Answers Click Here

7. Which of the following sets of connectives are complete in propositional logic?

  • {NAND}
  • {⊃}
  • {∧,¬}
  • {∨,¬}
Answer :-

8. A knowledge base (KB) written in a logic language is ______________ .

  • a set of sentences where all the sentences in that set are true
  • a set of sentences where some sentences may be false because we need the ability to represent what is false
  • none of these
Answer :-

9. In propositional logic, what does it mean to say that a KB entails P (symbolically, KB ⊨ P)?

  • When all the sentences in KB are true then P is necessarily true.
  • One can derive P from the sentences in the KB.
  • All of the above
Answer :-

10. What does (KB ⊢ P) mean?

  • KB entails P.
  • KB derives P.
  • All of the above.
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11. A proof or derivation in logic is ____________ .

  • a syntactic process that uses inference rules to generate new formulas from existing formulas
  • a syntactic process that does not bother with the truth values of the sentences that are begin read and/or derived
  • an evaluation function that uses the truth values of existing formulas to derive truth values for new formulas
Answer :-

12. Consider four proof procedures (derivation algorithms) A, B, C, D. The quality of the sentences derived by each procedure is depicted below.

Select the procedure(s) that are sound.

  • Procedure A
  • Procedure B
  • Procedure C
  • Procedure D
Answer :-

13. Select the procedure(s) that are complete.

  • Procedure A
  • Procedure B
  • Procedure C
  • Procedure D
Answer :-

14. Observation: dry vegetation causes wildfires in the Santa Monica Mountains.

D: There is dry vegetation.
W: There is a wildfire.

Which of the following is the correct logic-based representation of the connection between the presence of dry vegetation and the presence of wildfire?

(Hint: choose the formula that produces acceptable output under all scenarios: presence/absence of dry vegetation and presence/absence of wildfire.)

  • W ∧ D
  • W ∨ D
  • W ⊃ D
  • D ⊃ W
  • (W ⊃ D) ∧ (D ⊃ W)
Answer :-

15. Is the following argument valid?

If there is a wildfire then houses will burn to cinders.
The houses were burnt to cinders.
Therefore, there was a wildfire.

  • Yes
  • No
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16. Is the following argument valid?

If there is a wildfire then houses will burn to cinders.
The houses did not burn, they remained intact.
Therefore, there was no wildfire.
  • Yes
  • No
Answer :-

17. Is the following argument valid?

He must have fire insurance or he must have huge savings.
He has zero savings.
Therefore, he has fire insurance.
  • Yes
  • No
Answer :-

18. Is the following argument valid?

He must have fire insurance or he must have huge savings.
He has massive savings.
Therefore, he has no fire insurance.
  • Yes
  • No
Answer :-

19. Frege’s Propositional Calculus uses only ________________ and ___________ connectives

  • AND (∧)
  • EQUIVALENCE (≡)
  • IMPLIES (⊃)
  • NAND (↑)
  • NOR (↓)
  • NOT (￢)
  • OR (∨)
Answer :-

20. Modus Ponens _______________ .

  • is a proof procedure
  • is a valid inference rule
  • is used to compute the truth values of compound sentences
  • all of the above
Answer :- For Answers Click Here

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