NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 3 Assignment Answers 2025

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NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 3 Assignment Answers 2025

1. Which of the following are well formed formulas in propositional logic? where P, Q, R are proposition symbols.

  • P
  • P ¬Q
  • ¬¬¬¬¬P⊃¬¬¬¬¬Q
  • (P ⊃ Q) ¬∧ R
  • (P ⊃ Q) ∧ ¬R
  • ¬(P ∧ Q) ≡ (¬P ∧ ¬Q)
Answer :- For Answers Click Here

2. Select the sentence(s) that express the transitivity property of the equivalence connective (≡), in propositional logic? Where P, Q, R are proposition symbols.

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

3. Represent the formula (P ∧ (P ⊃ Q)) using NAND(↑) connective.

  • (P ↑ Q)
  • (P ↑ P) ↑ (Q ↑ Q)
  • (P ↑ Q) ↑ (P ↑ Q)
  • None of the above
Answer :-

4. KB entails Q (KB ⊨ Q) if and only if ____________ .

  • Q is necessarily true when at least one sentence in the KB is true
  • Q is necessarily true when all the sentences in the KB are true
  • at least one model of the KB is necessarily a model of Q
  • every model of the KB is necessarily a model of Q
Answer :-

5. Select the interpretations that are NOT models of the given KB.

 KB: { (P ⊃ Q) ⊃ (Q ⊃ R) }
  • { P:T, Q:T, R:T }
  • { P:T, Q:T, R:F }
  • { P:T, Q:F, R:T }
  • { P:T, Q:F, R:F }
  • { P:F, Q:T, R:T }
  • { P:F, Q:T, R:F }
  • { P:F, Q:F, R:T }
  • { P:F, Q:F, R:F }
Answer :-

6. Select the correct entailments.

KB: { (P ⊃ Q) ⊃ (Q ⊃ R) }
  • KB ⊨ (P ⊃ R)
  • KB ⊨ (Q ⊃ R)
  • KB ⊨ ((P ∧ Q) ⊃ R)
  • KB ⊨ (Q ⊃ (P ∨ R))
Answer :- For Answers Click Here

7. The fire chief said: “… Mel Gibson’s home was burnt down by a wildfire that was out of control …”

B: Mel Gibson’s home was burnt down.
W: There was a wildfire.
C: The wildfire was in control.

Express the fire chief’s statement in propositional logic. Which of the following representations (KBs) agree with the conclusion drawn by the fire chief?

  • KB2: { W, ¬C, B ⊃ (W ∧ ¬C) }
  • KB3: { W, ¬C, W ⊃ (¬C ⊃ B) }
  • KB4: { W, ¬C, (W ∧ ¬C) ⊃ B }
Answer :-

8. Select the sentences that can be derived from the given KB?

KB: { If the voter turnout is high and proof of citizenship is required for voting, then Don will win the election. If the election is rigged, then Don will not win the election. If proof of citizenship is not required for voting or favorable ballots are deleted, then the election is rigged. Don won the election. }

  • Favorable ballots were deleted.
  • Favorable ballots were not deleted.
  • Proof of citizenship was required for voting.
  • Proof of citizenship was not required for voting.
  • The voter turnout was high.
  • The voter turnout was not high.
Answer :-

9. Select the valid tableau expansion rules.

  • Rule 1
  • Rule 2
  • Rule 3
  • Rule 4
  • Rule 5
  • Rule 6
Answer :-

10. Which of these expansion trees show the correct application of tableau expansion rules?

  • Tree 1
  • Tree 2
  • Both trees
  • None of the above
Answer :-

11. Which of the expansion trees in the previous question show a proof of the statement ((P ⊃ Q) ⊃ (Q ⊃ R)) ⊃ (Q ⊃ (P ∨ R)) using Tableau Method?

  • Tree 1
  • Tree 2
  • Both trees
  • None of the above
Answer :-

12. After the Tableau Method halts, the expansion tree produced by the Tableau Method may contain _______________ .

  • fully expanded open branches
  • fully expanded closed branches
  • partially expanded open branches
  • partially expanded closed branches
Answer :- For Answers Click Here

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