##### Reference no: EM131444893

**Question 1.** (a) Solve the given puzzle using crypt arithmatic method.

B A S E

+ B A L L

G A M E S

(b) Apply uniform cost search Algorithm on given graph.

**Question 2.** (a) Consider the examples.

(i) If Triangle is equilateral then it is isosceles.

(ii) If Triangle is isosceles then two sides 'A' and 'B' are equal.

(iii) If 'AB' and 'AC' are equal then Angle 'B' and 'C' are equal.

(iv) ABC is an equilateral Triangle.

Prove that angle 'B' is equal to angle 'C' using inferencing techniques of modus ponen and Resolution.

**Question 3.** (a) Consider the knowledge base KB that contains the following propositional logic sentences.

Q ⇒ P

P ⇒ ¬ Q

Q v R

(i) Construct a Truth table trat shows the truth value of each sentence in KB and indicate the model in which the KB is true.

(ii) Does KB entail R ? Use the definition of entailment to justify your answer.

(iii) Does KB R ⇒ ¬ P entail ? Extend the truth table and usQ the definition of entailment to justify your answer.

(iv) Does KB Q ⇒ ¬ R entail ? Extend truth table and use the definition of entailment to justify your answer.

**Question 4.** (a) You have two neighbours, John and Mary, who have promised to call you at work when they hear the alarm. John always calls when he hears the alarm, but sometimes confuses the telephone ringing with the alarm and calls then, too. Mary on the other hand, likes rather loud music and sometimes misses the alarm altogether. Given the evidence of who has or has not called, we would like to estimate the probability of a burglary.

Draw a Bayesian network for this domain with suitable probability tables.

**Question 5.** (a) Consider the given Game Tree. Apply the Aplpha- Beta pruning algorithm and 10 decide, what is to be the next best move ? (Δ - max node , ∇- min node)