a) professor (Lucy) b) Vx (professor(x)= people(x)) c) dean (Fuchs) d) Vx (dean(x) = professor(x)) e) Vx (Vy (professor(x) a dean(y)= is-friend-of (y, x) v- knows (x, y))) f) Vx (3y (is-friend-of (y, x))) g) Vx (Vy (people(x) ^ people(y) a criticize (x, y)= is-friend-of (y, x))) h) criticize (lucy, Fuchs)

a) professor (Lucy) b) Vx (professor(x)= people(x)) c) dean (Fuchs) d) Vx (dean(x) = professor(x)) e) Vx (Vy (professor(x) a dean(y)= is-friend-of (y, x) v- knows (x, y))) f) Vx (3y (is-friend-of (y, x))) g) Vx (Vy (people(x) ^ people(y) a criticize (x, y)= is-friend-of (y, x))) h) criticize (lucy, Fuchs)

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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Let B(x) be the statement "X is a ball", R(x) be the statement "X is round and let S(x) be the statements "X is a soccer ball" where the domain consists of the whole world. Write the following sentences using predicates and qunitifiers: a) All balls are round b) Some soccer balls are round c) Some soccer balls are not round d) Every soccer ball is round e) A soccer ball is roundUser A for the universal quantifier symbol and E for the existential quantifier symbol
The Martian language can be written in the familiar Roman alphabet, which has 21 consonants (B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z) and 5 vowels (A, E, I, O, U). All Martian nouns begin with a consonant, followed by one or more vowel-consonant pairs. However, no consonant can appear more than once in a single noun, and no vowel can appear more than once in a single noun. For example, VUX, DIYOK, and ZOBALUT are possible Martian nouns, but X, VUV, DIYIK, and ZEZELAL are not. How many Martian nouns are possible? Your answer must be a number. Briefly explain your answer.
The Martian language can be written in the familiar Roman alphabet, which has 21 consonants (B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z) and 5 vowels (A, E, I, O, U). All Martian nouns begin with a consonant, followed by one or more vowel-consonant pairs. However, no consonant can appear more than once in a single noun, and no vowel can appear more than once in a single noun. For example, VUX, DIYOK, and ZOBALUT are possible Martian nouns, but X, VUV, DIYIK, and ZEZELAL are not. Recent expeditions to Mars have cast doubt on whether the Martian language can be written with exactly 21 consonants and 5 vowels. Suppose that Martian requires c consonants and v vowels, where c > 0, v > 0, and c > v. Express the number of possible Martian nouns in terms of c and v. Your answer need not be in closed form.
Let C(x) be the statement “x has a cat,” and let D(x) be the statement “x has a dog.” Let the domain consist of all students in this class. Express each of the following propositions in regular sentences.(a)∀x(C(x)→D(x)) (b)∀x(¬C(x)→D(x)) (c) (∃xC(x))∧(∀xD(x)) (d)∀x(C(x)⊕D(x))
Let B(x) be the statement "X is a ball", R(x) be the statement "X is round and let S(x) be the statements "X is a soccer ball" where the domain consists of the whole world. Write the following sentences using predicates and qunitifiers: d) Every soccer ball is round e) A soccer ball is roundUser A for the universal quantifier symbol and E for the existential quantifier symbol
Convert the following predicate calculus to English sentence. (∀X) (dog(X) → barks(X))
Find the most general unifier (if it exists): a) Marries (x, John), Marries (Elizabeth, y) b) Marries (thatperson, Mary), Marries (father (Me), mother (y))
4. Let N(x) be the statement “x has visited North Dakota,” where the domain consists of the students in your school. Express each of these quantifications in English. a) ∃x N(x) b) ∀x N(x) c) ˺∃x N(x) d) ∃x ˺N(x) e) ˺∀x N(x) f ) ∀x ˺N(x)
Let p, q and r be propositions: p: Jasper has sore eyes q: Jasper misses the last day of the board exam r: Jasper passes the board exam Write the following propositions in terms of the given connectives: a.) q→¬r b.) q ↔ p c.) p → q ⋀ ¬r
8. Let the universe of discourse be U = {−2,−1, 0, 1, 2}. Compute the negations for each of thefollowing statements, via transforming the negation connectives inward, such that the negationsymbols immediately precede predicates. Thereafter, determine whether each of the negatedstatement is true or false. Note that x and y range over U.(a) ∀x∃y(x + y = 1).(b) ∃x∀y(x + y = −y).(c) ∀x∃y(xy ≥ y).(d) ∃x∀y(x ≤ y).
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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.