## NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 2 Assignment Answers 2024

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

- Shiva, please take us to Baijnath temple.
- Shiva will take us to Baijnath temple.
- Baijnath temple is surrounded by mountains.
- Does ChatGPT know the answers to all the questions?
- ChatGPT knows the answers to all the questions.
- The number 4 is a prime number.

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2. State true or false. Induction and Abduction are used in day to day situations because both together provide a sound inference method.

- True
- False

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3. What does the statement **(P ⊃ Q)** convey? (Note: it is very very important for beginners to understand and internalise the conditional-statement.)

- When P is true then Q is true.
- When P is false then Q is false.
- When Q is true then P is true.
- When Q is false then P is false.

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4. Model the situation “a number x that is greater than 10 is greater than 5 as well” in Propositional Logic. (Hint: select the formula that remains meaningful for various values of x.)

**A: number x is greater than 5.****B: number x is greater than 10.**

- A ∧ B
- A ∨ B
- A ⊃ B
- B ⊃ A

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5. Model the sentence “Snapdragons bloom only in winter” in Propositional Logic.

**B: Snapdragons are in bloom.****W: It is winter.**

- B ∧ W
- B ∨ W
- B ⊃ W
- W ⊃ B

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6. Select the valid rules of substitution.

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

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7. Select the valid rules of inference.

- {P, P ⊃ Q} ⊢ Q
- {P ∧ Q} ⊢ (P ∨ Q)
- {P ∨ Q, ¬Q} ⊢ P
- {P ⊃ Q, ¬Q} ⊢ ¬P

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8. A knowledge base (KB) is __________ .

- a collection of all human knowledge (a large language model like ChatGPT)
- a set of sentences where all the sentences are true
- a set of sentences where some sentences may be false because we need the ability to say what is false
- All of the above

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9. A proof or derivation in logic __________ .

- involves preparing the truth table for the sentence P
- is a syntactic process that uses inference rules to generate new formulas from the existing formulas in a KB
- is a syntactic process that does not bother with the truth values of the sentences that are read and/or derived
- is a syntactic process that analyses the real world meaning of the sentence that we wish to prove/derive

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10. What does it mean to say that a KB entails P, which is written as (KB ⊨ P), in Propositional Logic?

- 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.

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11. Which of the following statements about entailments are correct?

- {P, P ⊃ Q} ⊨ Q
- {Q, P ⊃ Q} ⊭ P
- {¬P, P ⊃ Q} ⊭ ¬Q
- {¬Q, P ⊃ Q} ⊨ ¬P

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

- {⊃}
- {⊃,¬}
- {∧,¬}
- {∧,∨,¬}

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13. What does (KB ⊢ P) mean?

- KB entails P
- .KB derives P.
- All of the above.

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14. If a proof procedure (derivation algorithm) in logic is complete then __________ and __________ . Choose the relevant two options to fill in the blanks.

- it can derive only the true sentences
- it can derive all the true sentences
- it may derive some false sentences
- it may not derive all the true sentences

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15. If a proof procedure (derivation algorithm) in logic is sound then __________ and __________ . Choose the relevant two options to fill in the blanks.

- it can derive only the true sentences
- it can derive all the true sentences
- it may derive some false sentences
- it may not derive all the true sentences

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16. A tautological formula in propositional logic __________ .

- is a sentence that evaluates to true when its variables are set to true
- is a sentence that evaluates to true when its variables are set to any combination of truth values
- is used to test whether a rule of inference is valid or not
- is used to test whether a rule of substitution is valid or not

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17. Is the following argument valid?

He must sow wheat or he must plant sugarcane.

He planted sugarcane.

Therefore, he did not sow wheat.

- Yes
- No

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18. Is the following argument valid?

Rain brings happiness to farmers.

It is raining.

Therefore, farmers are happy.

- Yes
- No

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19. Is the following argument valid?

Bountiful harvest brings happiness to farmers.

Farmers are happy.

Therefore, the harvest was bountiful.

- Yes
- No

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20. Is the following argument valid?

High demand for wheat brings happiness to farmers.

Farmers are unhappy.

Therefore, demand for wheat is low.

- Yes
- No

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