Q. Which of the following arguments are not valid?

(a) “If Gora gets the job and works hard, then he will be promoted. If Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard”.

(b) “Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty”.

(c) If n is a real number such that n>1, then n^2>1. Suppose that n^2>1, then n>1.

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Q. Let P(m,n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions.

(a) ∃m ∀n P(m,n)        (b) ∀n P(1,n)             (c) ∀m ∀n P(m,n)

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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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