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

## 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.
`Answer :-  For Answer Click Here`

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
`Answer :-  For Answer Click Here`

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.
`Answer :- `

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
`Answer :- `

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
`Answer :- `

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)]
`Answer :-  For Answer Click Here`

7. Select the valid rules of inference.

• {P, P ⊃ Q} ⊢ Q
• {P ∧ Q} ⊢ (P ∨ Q)
• {P ∨ Q, ¬Q} ⊢ P
• {P ⊃ Q, ¬Q} ⊢ ¬P
`Answer :- `

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
`Answer :- `

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
`Answer :- `

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.
`Answer :-  For Answer Click Here`

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
`Answer :- `

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

• {⊃}
• {⊃,¬}
• {∧,¬}
• {∧,∨,¬}
`Answer :-  For Answer Click Here`

13. What does (KB ⊢ P) mean?

• KB entails P
• .KB derives P.
• All of the above.
`Answer :- `

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
`Answer :- `

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
`Answer :-  For Answer Click Here`

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
`Answer :- `

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
`Answer :- `

18. Is the following argument valid?

Rain brings happiness to farmers.
It is raining.
Therefore, farmers are happy.

• Yes
• No
`Answer :-  For Answer Click Here`

19. Is the following argument valid?

Bountiful harvest brings happiness to farmers.
Farmers are happy.
Therefore, the harvest was bountiful.

• Yes
• No
`Answer :- `

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
`Answer :- For Answer Click Here`