PREVIOUS YEAR SOLVED PAPERS - November 2017 Paper 3

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56. If b is the branching factor and m is the maximum depth of the search tree, what is the space complexity of greedy search?

  • Option : C
  • Explanation :
    1. In binary tree branching factor is 2 and space complexity for height n is O(2n).
    2. In ternary tree branching factor is 3 and space complexity for height n is O(3n).
    3. If branching factor is b and height is m for search tree then space complexity of greedy search is O(bm).
    So, option (C) is correct.
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57. Let P, Q, R and S be Propositions. Assume that the equivalences P ⇔ (Q ∨ ¬ Q) and Q ⇔ R hold. Then the truth value of the formula (P ∧ Q) ⇒ ((P ∧ R) ∨ S) is always:

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58. “If X, then Y unless Z” is represented by which of the following formulae in propositional logic?

  • Option : B
  • Explanation :
    If X then Y is represented by X → Y one more condition is unless Z, it will be included in X, so X then Y unless Z is represented by (X ^ ¬Z) → Y. So, option (B) is correct.
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59. Consider the following two well-formed formulas in prepositional logic.
F1 : P ⇒ ¬ P
F2 : (P ⇒ ¬ P) ∨ (¬ P ⇒ P)
Which of the following statements is correct?

  • Option : A
  • Explanation :
    F1: P → ¬P = ¬P(¬P) + P¬(¬P) = ¬P + P is satisfiable.
    F2: (P ⇒ ¬ P) ∨ (¬ P ⇒ P) = (¬P(¬P) + P¬(¬P)) v (P¬(¬P) + ¬P(¬P) ) = satisfiable v satisfiable is satisfiable.
    So, option (A) is correct.
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60. Standard planning algorithms assume environment to be __________.

  • Option : A
  • Explanation :
    Standard planning algorithms assume environment to be both deterministic and fully observable. So, option (A) is correct.
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Related Quiz.
November 2017 Paper 3