Q. "If my computations are correct and I pay the electric bill, then I will run out of money. If I don't pay the electric bill the power will be turned off. Therefore, if I don't run out of money and the power is still on then my computations are incorrect."
Convert this argument into logical notations using the variables c, b, r, p for propositions of computations, electric bills, out of money and the power respectively. (Where  ¬ means NOT)

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Q. Match the following:

(a) (p →q) ⇔ (¬q → ¬p) (i) Contrapositive

(b) [(p ∧q) →r ]⇔ [p→ (q →r)] (ii) Exportation law

(c) (p →q)⇔ [(p ∧ ¬q) →o] (iii) Reductio ad absurdum

(d) (p⇔q)⇔ [(p →q) ∧(q→p)] (iv) Equivalence

code:
(a)  (b)  (c)   (d)

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Q. Consider a proposition given as :

" x ≥ 6, if  x2 ≥ 25 and its proof as:

If x ≥ 6, then x2 = x· x= 6· 6=36 ≥25

Which of the following is correct w.r.to the given proposition and its proof ?
(a) The proof shows the converse of what is to be proved.
(b) The proof starts by assuming what is to be shown.
(c) The proof is correct and there is nothing wrong.

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Q. The clausal form of the disjunctive normal form ¬ A ˅ ¬ B ˅ ¬ C ˅ D is :

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Q. Which of the following is false for the programming language PROLOG?

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Q. Which one of the following is true?

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Q. Match the following :

List – I List – II

(a) Intelligence (i) Contextual, tacit, transfer needs learning

(b) Knowledge (ii) Scattered facts, easily transferable

(c) Information (iii) Judgmental

(d) Data (iv) Codifiable, endorsed with relevance and purpose

code:
a b c d

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Q. Which of the following statements is true for Branch - and - Bound search?

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Q. Match the following with respect to heuristic search techniques:

List – I List – II

(a) Steepest - accent Hill Climbing (i) Keeps track of all partial paths which can be candidate for further exploration

(b) Branch - and - bound (ii) Discover problem state(s) that satisfy a set of constraints

(c) Constraint satisfaction (iii) Detects difference between current state and goal state

(d) Means - end - analysis (iv) Considers all moves from current state and selects best move

code:
a b c d

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Q. In the Hungarian method for solving assignment problem, an optimal assignment requires that the maximum number of lines that can be drawn through squares with zero opportunity cost be equal to the number of :

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Q. Given the following statements with respect to linear programming problem :

S1: The dual of the dual linear programming problem is again the primal problem

S2: If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution.

S3: If either the primal or dual problem has a finite optimal solution, the other one also possesses the same, and the optimal value of the objective functions of the two problems are equal.

Which of the following is true?

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

Class C1 : [1 1.5]   [1 -1.5]

Class C2 : [-2 2.5]   [-2 -2.5]

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

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Q. Which one of the following describes the syntax of prolog program ?

I. Rules and facts are terminated by full stop (.)
II. Rules and facts are terminated by semicolon (;)
III. Variables names must with upper case alphabets.
IV. Variables names must start with lower case alphabets.

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Q. Match the following: 

List-I                                                                          List-II

a. Expert systems                                                    i.  Pragmatics

b. Planning                                                               ii.  Resolution

c. Prolog                                                                   iii. Means-end analysis

d. Natural language processing                          iv. Explanation facility

Codes:

a       b       c       d

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Q. STRIPS addresses the problem of efficiently representing and implementation of a planner. It is not related to which one of the following ?

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Q. _________ predicate calculus allows quantified   variables   to   refer  to objects in the domain of discourse and not to predicates or functions.

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Q. ________ is used in game trees to reduce the number of branches of the search tree to be traversed without affecting the solution.

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Q. Which of the following special cases does not require reformulation of the problem in order to obtain a solution ?

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Q. The given maximization assignment problem can be converted into a minimization problem by

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Q. Consider the fractional knapsack instance n = 4, (p1, p2, p3, p4) = (10, 10, 12, 18). (w1, w2, w3, w4) = (2, 4, 6, 9) and M = 15. The maximum profit is given by

(Assume p and w denotes profit and weight of objects respectively)

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