Artificial Intelligence: Knowledge Representation And Reasoning Week 2 Answer
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Nptel AI Knowledge Representation And Reasoning Week 2 Answer (Jan-Apr 2025)
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1) A sentence in logic is a statement that in principle has a truth value. Which of the following are sentences in logic?
(a) Did Joe pardon his son?
(b) Joe said he will not pardon his son.
(c) Joe did not pardon his son.
(d) Please sign a law banning voter ID.
(e) Governor signed a law banning voter ID.
2) Select the reasoning method(s) that lead to logically sound arguments.
(a) Abduction
(b) Deduction
(c) Both of the above
(d) None of the above
3) Select the formulas that are tautologies.
4) Given three formulas PP, QQ, and RR, a rule of inference such as {P,Q}⊢R\{P, Q\} \vdash R is said to be valid if and only if:
(a) ((P∧Q) ⟹ R)((P \land Q) \implies R) is satisfiable
(b) ((P∧Q) ⟹ R)((P \land Q) \implies R) is a tautology
(c) (¬P∨¬Q∨R)(\neg P \lor \neg Q \lor R) is satisfiable
(d) (¬P∨¬Q∨R)(\neg P \lor \neg Q \lor R) is a tautology
(e) (P∧Q∧¬R)(P \land Q \land \neg R) is satisfiable
(f) (P∧Q∧¬R)(P \land Q \land \neg R) is a tautology
5) Select the valid rules of substitution.
6) Select the valid rules of inference.
7) Which of the following sets of connectives are complete in propositional logic?
8) A knowledge base (KB) written in a logic language is
(a) A set of sentences where all the sentences in that set are true
(b) A set of sentences where some sentences may be false because we need the ability to represent what is false
(c) None of these
9) In propositional logic, what does it mean to say that a KB entails PP (symbolically KB⊨PKB \models P)?
(a) When all the sentences in KBKB are true, then PP is necessarily true
(b) One can derive PP from the sentences in the KBKB
(c) All of the above
10) What does KB⊢PKB \vdash P mean?
(a) KBKB entails PP
(b) KBKB derives PP
(c) All of the above
11) A proof or derivation in logic is
(a) A syntactic process that uses inference rules to generate new formulas from existing formulas
(b) A syntactic process that does not bother with the truth values of the sentences being read and/or derived
(c) An evaluation function that uses the truth values of existing formulas to derive truth values for new formulas
12) Consider four proof procedures (derivation algorithms) A, B, C, D. The quality of the sentences derived by each procedure is depicted below.
Select the procedure(s) that are sound.
(a) Procedure A
(b) Procedure B
(c) Procedure C
(d) Procedure D
13) Select the procedure(s) that are complete.
(a) Procedure A
(b) Procedure B
(c) Procedure C
(d) Procedure D
14) Observation: Dry vegetation causes wildfires in the Santa Monica Mountains.
DD: There is dry vegetation.
WW: There is a wildfire.
Which of the following is the correct logic-based representation of the connection between the presence of dry vegetation and the presence of wildfire? (Hint: choose the formula that produces acceptable output under all scenarios: presence/absence of dry vegetation and presence/absence of wildfire.)
15) Is the following argument valid?
If there is a wildfire, then houses will burn to cinders.
The houses were burnt to cinders.
Therefore, there was a wildfire.
(a) Yes
(b) No
16) Is the following argument valid?
If there is a wildfire, then houses will burn to cinders.
The houses did not burn; they remained intact.
Therefore, there was no wildfire.
(a) Yes
(b) No
17) Is the following argument valid?
He must have fire insurance or he must have huge savings.
He has zero savings.
Therefore, he has fire insurance.
(a) Yes
(b) No
18) Is the following argument valid?
He must have fire insurance or he must have huge savings.
He has massive savings.
Therefore, he has no fire insurance.
(a) Yes
(b) No
19) Frege’s Propositional Calculus uses only __________and __________connectives.
(a) AND (∧\land)
(b) EQUIVALENCE ( ⟺ \iff)
(c) IMPLIES ( ⟹ \implies)
(d) NAND (↑\uparrow)
(e) NOR (↓\downarrow)
(f) NOT (¬\neg)
(g) OR (∨\lor)
20) Modus Ponens___________.
(a) Is a proof procedure
(b) Is a valid inference rule
(c) Is used to compute the truth values of compound sentences
(d) All of the above
Nptel AI Knowledge Representation And Reasoning Week 2 Answer (Jan-Apr 2025)
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