Question 10 Write the following statements in symbolic form using universal and existential quantifiers and suitable predicates and logical operators, using the following: Let A be the set of all animals; Let P(a) be the predicate "The animal a has a horn"; What is the correct, formal way of writing: "Not all animals have horns"? VaEAl-P(a) 3aEA P(a) VaEA P(a) JaEAl-P(a) Question 11 Write the following statements in symbolic form using universal and existential quantifiers and suitable predicates and logical operators, using the following: Let S be the set of all shapes; Let P(s) be the predicate "The shape s is a rectangle"; Let Qls) be the predicate "The shape s has 4 angles". What is the correct, formal way of writing: "If the shape s has 4 angles, then it is a rectangle"? VSESI-P(s)--Q(s) VSES P(s)-Q(s) VSES|Q(s)--P(s) VSESIQ(s)-P(s)

Question 10 Write the following statements in symbolic form using universal and existential quantifiers and suitable predicates and logical operators, using the following: Let A be the set of all animals; Let P(a) be the predicate "The animal a has a horn"; What is the correct, formal way of writing: "Not all animals have horns"? VaEAl-P(a) 3aEA P(a) VaEA P(a) JaEAl-P(a) Question 11 Write the following statements in symbolic form using universal and existential quantifiers and suitable predicates and logical operators, using the following: Let S be the set of all shapes; Let P(s) be the predicate "The shape s is a rectangle"; Let Qls) be the predicate "The shape s has 4 angles". What is the correct, formal way of writing: "If the shape s has 4 angles, then it is a rectangle"? VSESI-P(s)--Q(s) VSES P(s)-Q(s) VSES|Q(s)--P(s) VSESIQ(s)-P(s)

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 p, q, and r be the propositions p: You started a new video game this week. q: You finished all its quests.r: You didn’t win the platinum trophy.Express each of these propositions as an English sentence.¬p → ¬q(p ∧ q) → (¬r)((¬p) → (¬q)) ∨ (q → (¬r))(p ∧ q) ∨ (¬q ∧ r)
Answer the following questions about the given statement:∀t : Trainers • ∃c : Course • (t,c) ∈Teaches ∧c.time = 2•What does this statement mean?•Is this statement a set or a predicate?•What does the statement evaluate to based on the current system state? Examples for reference:•∃g : Owner • g.name = gymowner ∧g.email = test-There exists an owner with the name gymowner and email test-predicate-false•{c : Course |∃co : Customer • (co,c) ∈Books}-Set of all Courses which are booked by a customer-set-{Boxing,WeightLifting,Yoga1,Wrestling}•{t : Trainer |#{c : Course |(t,c) ∈Teaches}>1}-Set of all Trainers who teach more than 1 class.-set-{Trainer 2}
Premise 1: All the cups in my house are green. Premise 2: I am drinking from a green cup. Conclusion: I must be at home. Decide whether the above argument is inductive or deductive. If the above argument is inductive, decide if it is strong or weak. Select not applicable if the argument is deductive. If the above argument is deductive, decide if it is valid or invalid. Select not applicable if the argument is inductive.
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When a Predicate has only a single Clause, which of the following Clause coverage criteria is enough to cover the Clause. a. General Inactive Clause Coverage b. Restricted Active Clause Coverage c. General Active Clause Coverage d. Predicate Coverage e. Combinatorial Clause Coverage
For the following conditional statements, write (i) the contrapositive of the statement (ii) the converse of the statement, and (iii) the negation of the statement.In part (a), your answer should be written in English (not in propositional logic).For (a), you might have to use DeMorgan’s Laws as part of the process.(a) (6 marks) If the schools are open and the roads are safe, then the game is not cancelled
Exhibit the structure of the following statements by transforming them into a first-order formula,indicating the interpretation of predicates and the domain. For example the statement There isno greatest integer can be transformed into ¬∃x, ∀y, P(x, y) where P(x, y) is the predicate x ≥ y,the domain being the integers.Do not try to prove them (it may not be possible!).1. Every integer can be written as the sum of 2 squares.2. Every positive real number has a square root.3. The cosine function has zeroes.4. The cosine function has at least two distinct zeroes.5. There is a neutral element1for multiplication in real numbers.6. Every odd square can be written as the sum of three odd numbers.
c) Translate the following English sentence into predicate logic. Use the predicates listed. “All CS students take at least two classes". Let the domain of discourse be all people and all courses CS(x) := True if x is a CS student Takes(x,y) := True if student x has taken course y Equals(x.y) := True if x equals y.
Write the following English statements using the following predicates and any needed quantifier. The domain of all variables are all at the school S(x): x is a student F(x): is a faculty member A(x, y): x has asked y a question Every student has asked Dr. Lee a question
3. Let S(x) be the statement "x studied for the exam" and H(x, y) be the statement "x scored higher than y in the exam," where the domain of x and y consists of all students in this class. Which logical expression corresponds to the following statement? "Every student in this class who studied for the exam scored higher in the exam than every student who did not study for the exam." a. VxVy (H (x, y) → (S(x) ^ ¬S(y))) b. VxVy(S(x)^¬S(y) ^ H (x, y)) c. VxVy((S(x) ^ ¬S(y)) → H (x, y)) d. VxVy((S(x) → ¬S(y)) → H (x, y))
Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) D(x): x is a day S(x): x is sunny R(x): x is rainy M: Monday T: Tuesday 1.All animals are dogs. 3.Some animals are not cats. 4.Every animal that is a dog is not a cat. 5.Some animals are dogs and cats. 6.No animal is both a dog and a cat. 7.An animal is always a dog only if it is a cat. 8.No animals are dogs. 9.Meg is a cat; all animals are cats. 10.Meg and Alex are both cats. 11.If one animal is a cat, then every animal will be a cat.
5. Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives. (1) No one is perfect. (11) Not everyone Is perfect. (111) All your friends are perfect. (Iv) At least one of your frlends is perfect.