## NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Assignment Answers 2024

1. In propositional logic, NAND stands for NOT AND, and NOR stands for NOT OR. Which of the following are propositional logic sentences that are composed from the atomic sentences A,B,C,D?

- (A ¬(B ⊃ C))
- A ¬∧ B
- A ¬∨ C
- B ¬⊃ C
- ¬(A ∧ B)
- ¬(A ∨ C)
- ¬¬D

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2. Let the propositional variables A, B, and C denote three distinct statements that are equivalent to each other, then we can use the propositional formula (A ≡ B ≡ C) to express the equivalence between A, B, and C.

- True
- False

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3. Represent the formula ¬[(A ⊃ B) ⊃ (P ⊃ Q)] using only the connectives {¬,∧}.

- A ∧ ¬B ∧ ¬(P ∧ ¬Q)
- ¬A ∧ B ∧ P ∧ ¬Q
- ¬(A ∧ ¬B) ∧ P ∧ ¬Q
- ¬(A ∧ ¬B) ∧ ¬P ∧ ¬Q

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4. A model for a KB in propositional logic is a list of ** __**____________ .

- truth values assigned to all sentences in the KB
- truth values assigned to all atomic propositions such that all sentences in the KB evaluate to true
- all atomic propositions in the KB
- all atomic propositions in the KB and their negations

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5. Select the correct option.

KB: { (A ∨ B) ⊃ (A ∧ B) }

- KB ⊨ (A ⊃ B)
- KB ⊨ (B ⊃ A)
- KB ⊨ (A ≡ B)
- All of the above

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

KB: { If there is no balance or the battery is dead then Kailash cannot make a call. If the battery is not charged then the battery is dead. Kailash made a call. Therefore, the battery was charged. }

- Kailash did not make a call.
- Kailash made a call.
- The battery is dead.
- The battery is not dead.
- The battery is charged.
- The battery is not charged.
- The phone has balance.
- The phone has no balance.

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7. Let α, β, γ, and δ be formulas over the set of propositions {P, Q, R}. Given the conjunction (α ∧ β ∧ γ ∧ ¬δ) as input, the Tableau Method may be used to show that ** __**__________.

- the conjunction is satisfiable
- the conjunction is unsatisfiable
- (α ∧ β ∧ γ) ⊃ δ is a tautology
- δ can be derived from the formulas α, β, γ

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8. Select the valid tableau expansion rules.

- Rule 1
- Rule 2
- Rule 3
- Rule 4
- Rule 5
- Rule 6

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

- Tree 1
- Tree 2
- Both 1 and 2
- None of the above

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10. Which of the tableau expansion trees in the previous question show a proof, by Tableau Method, of the statement (P ⊃ (Q ⊃ R)) ⊃ ((P ⊃ Q) ⊃ (P ⊃ R))?

- Tree 1
- Tree 2
- Both 1 and 2
- None of the above

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11. In an expansion tree produced by the Tableau Method ** __** .

- a closed branch produces a model for the formula at the root of the tree
- a closed branch produces a model for the NEGATION of the formula at the root of the tree
- a fully expanded open branch produces a model for the formula at the root of the tree
- a fully expanded open branch produces a model for the NEGATION of the formula at the root of the tree

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