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## NPTEL An Introduction to Artificial Intelligence Week 7 Assignment Answers

**Q1. In propositional logic, what is the identity of the conjunction and disjunction operators respectively?**

**Answer:** b

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**Q2. Consider a SAT formula where DPLL algorithm, as discussed in class. The idea of a “pure” variable allowed us to improve our search for satisfying assignments. Consider the following CNF formula:(𝑎 ∨¬𝑏 ∨𝑐) ∧(¬𝑏 ∨¬𝑐 ∨𝑑) ∧(𝑐 ∨¬𝑒 ∨¬𝑑) ∧(¬𝑎 ∨𝑒) ∧(𝑎 ∨ 𝑑).**

**What variable would be set by the DPLL algorithm and what would be its value?**

**Answer:** c. b,True (suggested answer)

**Q3. Take S1: (¬a v b), and S2 : (a -> b). Which of the following is(are) tautologies?**

**Answer:** b. S1 |=S2 , d. S2 |= S1

**Q4.** *_* encodes the grammar that represents all sentences of a language like propositional logic?

**Answer:** c

**Q5. Suppose S1 implies S2 and S1 is unsatisfiable. Then what can be said about S2:**

**Answer:** a

**Q6. Krushal wishes to make a solver which can prove Boolean statements. He comes up with an algorithm which can achieve this. After testing the algorithm on 10000 statements, he discovers that his algorithm is accurate 99.9 % of the time and 0.1 % it can give wrong results i.e a true statement as false or vice-versa. Which of the following options are correct?**

**Answer:** a , c

**Q7. Consider the following CNF formula. If the number of unit literals in the formula is x and the number of pure literals is y, then which of the following is true about x + 2y? {{¬b c}{¬c}{a ¬b e}{d b}{e a ¬c}}**

**Answer:** a, b, c

**Q8. GSAT is an example of which of the following?**

**Answer:** b.

**Q9. Which of the following is an equivalent CNF formula of (p → q) → (q → r)?**

**Answer:** a.

**Q10. Drokoland is a place where everyone is honest but a lot of crime happens. For a theft case, the police catch 3 suspects, A, B, and C.**

A says “C is innocent. B is guilty”

B says “If A is guilty then so is C”

C says “I am innocent. Atleast one of the other two is guilty”

Assume that everyone speaks the truth. You have the following three propositions now-

- P: A is innocent, (¬ P): A is guilty
- Q: B is innocent, (¬ Q): B is guilty
- R: C is innocent, (¬ R): C is guilty

Which of the following propositions can be proved by resolving with the ones obtained from the above dialogue given?

a. P

b. ¬ P

c. Q

d. ¬ Q

e. R

f. ¬ R

**Answer:** b. ¬ P

c. Q

f. ¬ R

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