B= (b1,b2,...,bn). Let I, be the set of integers: {1,2,...,n}. Make a formal assertion for each of the following situations, using quantifiers with respect to I,. For example, Vi E I,:Vj€I,:a;=aj asserts that all letters in A are identical. You may use the relational operators "=", "#", and "". as well as our usual operators: "V". "A". (< is "less than" for English letters: c

B= (b1,b2,...,bn). Let I, be the set of integers: {1,2,...,n}. Make a formal assertion for each of the following situations, using quantifiers with respect to I,. For example, Vi E I,:Vj€I,:a;=aj asserts that all letters in A are identical. You may use the relational operators "=", "#", and "". as well as our usual operators: "V". "A". (< is "less than" for English letters: c

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Please answer the following question in depth with full detail. Consider the 8-puzzle that we discussed in class. Suppose we define a new heuristic function h3 which is the average of h1 and h2, and another heuristic function h4 which is the sum of h1 and h2. That is, for every state s ∈ S: h3(s) =h1(s) + h2(s) 2 h4(s) =h1(s) + h2(s) where h1 and h2 are defined as “the number of misplaced tiles”, and “the sum of the distances of the tiles from their goal positions”, respectively. Are h3 and h4 admissible? If admissible, compare their dominance with respect to h1 and h2, if not, provide a counterexample, i.e. a puzzle configuration where dominance does not hold.
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Exercise 1.A set W of strings of symbols is defined recursively by a, b, and d belong to W. If x belongs to W, so does a(x)d. Provide 3 strings made of 3 letters each belonging to W and show the procedure used to obtain them. Provide 3 strings made of at least 5 letters each belonging to W and show the procedure used to obtain them.
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5 A. Let * be a new logical connective such that p * q does not hold if and only if p and q are either both false or both true. (i) Write down the truth table for p * q (ii) Write down the truth table for (p * p) * (q * q). (iii) Does the table in (b) coincide with a table in *Truth table available on the given image* (By "Coincide" we mean that the respective columns of T and F values are the same) B. Construct a formula in CNF based on each of the following truth tables: *Truth table available on the given image* C. Compute CNF (NNF ( IMPL_FREE ¬(p → ( ¬ (q ∧ ( ¬p → q))))))
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