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

Join Our WhatsApp Group Join Now
Join Us On Telegram Join Now

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