Q. Match the following terms:

List - I                                     List - II
(a) Vacuous proof       (i) A proof that the implication p→q is true
based on the fact that p is false
(b) Trivial proof             (ii) A proof that the implication p→q is true
based on the fact that q is true
(c) Direct proof             (iii) A proof that the implication p→q is true
that proceeds by showing that q must be true
when p is true.
(d) Indirect proof          (iv) A proof that the implication p→q is true
that proceeds by showing that p must be false
when q is false.

Codes:
      (a)  (b)   (c)    (d)

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Q. Consider the compound propositions given below as:

(a) p˅~(p˄q)                  (b) (p˄~q)˅~(p˄q)                 (c) p˄(q˅r)

Which of the above propositions are tautologies?

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Q. Which of the following property/ies a Group G must hold, in order to be an Abelian group?

(a) The distributive property
(b) The commutative property
(c) The symmetric property

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Q. Given the following set of prolog clauses:

father(X, Y):
parent(X, Y),
male(X),
parent(Sally, Bob),
parent(Jim, Bob),
parent(Alice, Jane),
parent(Thomas, Jane),
male(Bob),
male(Jim),
female(Salley),
female(Alice).

How many atoms are matched to the variable ‘X’ before the query
father(X, Jane) reports a Result?

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Q. Forward chaining systems are ............. where as backward chaining systems are ................

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Q. A horn clause is ......................

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Q. In Propositional Logic, given P and P→Q, we can infer .................

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Q. Reasoning strategies used in expert systems include ...............

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Q. Language model used in LISP is .................

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Q. In constraint satisfaction problem, constraints can be stated as ...................

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Q. Consider the two class classification task that consists of the following points :

Class C1: [-1, -1], [-1, 1], [1, -1]
Class C2: [1, 1]

The decision boundary between the two classes C1 and C2 using single perceptron is given by :

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Q. How many different truth tables of the compound propositions are there that involve the propositions p & q ?

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Q. The notation ∃!xp(x) denotes the proposition "there exists a unique x such that P(x) is true".
Give the truth values of the following statements :

I. ∃!xP(x) → ∃xP(x)
II. ∃!x ¬ P(x) → ¬∀xp(x)

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Q. Give a compound proposition involving propositions p, q and r that is true when exactly two of p, q and r are true and is false otherwise.

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Q. The quantification ∃!x P(x) denotes the proposition “There exists a unique x such that P(x) is true”, express the quantification using universal and existential quantifications and logical operators:

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Q. Which of the following is a correct predicate logic statement for “Every Natural number has one successor” ?

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Q. α – β cutoffs are applied to .............

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Q. Assume that each alphabet can have a value between 0 to 9 in a cryptoarithmetic problem 
   CROSS+ROADS
--------------
DANGER
--------------
Which of the following statement is true ?

(i) No two alphabets can have the same numeric value.
(ii) Any two alphabets may have the same numeric value.
(iii) D = 0
(iv) D = 1

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Q. Which of the following is not a part of an expert system shell ?

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Q. The Blocks World Problem in Artificial Intelligence is normally discussed to explain a ..................

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