Answered: Given the following premises: (1) Vx…

Given the following premises: (1) Vx (A(x)→ B(x)) (2) Vx (B(x)→ C(x)) Prove the conclusion Vx (A(x) → C(x)) using the rules of first-order logic. Show your step-by-step reasoning.

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

See similar textbooks

Related questions

Q: a. Y = AC + ABC + ABC (reduce to one literal) b. Y = AB + ABC + (Ã+ C) (reduce to one literal) c. Y…

A: Below is the answer of all parts. hope this will be helpful for you..

Q: Consider the first-order logic formula ∃x (P(a, x) ˄ P(x, b)) and the interpretation domain D =…

A: In the first-order logic formula ∃x (P(a, x) ˄ P(x, b)): The variable x is a bound variable because…

Q: value of each ollowing interpretation where the domain consists of people, M(x, y) is "x is the…

A: Hi check below for the multiple choice question answers with the explanation.

Q: Prove the following proposition,

A: Proposition: A statement that is either true or false. p —> q , p V w , q —>~s , s => w We…

Q: ((P→R)∧(Q→Z))∧(P∨Q)→(Z∨R)

A: Consider the given expression ((P→R)∧(Q→Z))∧(P∨Q)→(Z∨R)

Q: Using predicate logic, prove the following argument. (Hint: The deductionmethod still…

A: The following inference rules will be used to prove the given argument: Modes ponens: |P → Q| Λ…

Q: Show that ¬(p → q) → ¬q is a tautology using rules (not a truth table

A: The given expression is a tautology. I am proving by rules. Please find hand written submission in…

Q: Prove the predictive logic statement is valid: (∀ x)(P(x) → Q(a)) ∧ (∃ y)(P(y)) → Q(a)

A: Given, The predictive logic statement: (∀ x)(P(x) → Q(a)) ∧ (∃ y)(P(y)) → Q(a) The given predictive…

Q: You are given the following sentences in propositional logic. Convert them to CNF and prove that "C…

A: Answer :

Q: Prove that the following logic statement is logically true using proof by contradiction:…

A: Proof by contradiction: In this method assume that the opposite statement is true. At last it is…

Q: (а) -(Ал -А) (b) -А — (А > В) (с) AV -A

A: 1) ¬(A^¬A) =¬A V ¬(¬A) Using DeMorgan's law =¬A V A = T…

Q: Prove the following theorem in the first-order logic Hilbert system: E(Væ A = -(B =→ 3x A)) = ¬V¤ A.

A: The solution for the above given question is given below:

Q: undefined terms. -two monkeys climb exact ere are exactly four monke ry tree is climbed by exact+…

A: Let us solve the given problem in the next steps.

Q: Use a truth table to determine if the following is a logical equivalence: ( q → ( ¬ q → ( p ∧ r )…

Q: how that (RA4) is independent of the other axioms of RA. (RA = Robinson's Arithmetic) Hint. Try…

A: SUMMARY: - hence we discussed all the points.

Q: Part V Construct a formal proof of validity for each of the following using CP and/or RAA. A) 1. A→…

Q: Use Tableaux algorithm to verify, whether formula (A→B)∧(A→(B→C))→(A→C) is derivable in classical…

A: Summary: The Tableaux Method replaces the statements "X is true" and "X is false" with their…

Q: Apply the Horn(φ) algorithm to the following Horn formulas. a. (p → q)∧(p ∧ q → r)∧(⊤ → r) b. (⊤ →…

A: A Horn formula is a propositional formula formed by conjunction of Horn clauses.This algorithm also…

Q: ng is/are tautology: ) (b) (a^ b)-→ (bv c) c) (d) (a b) → (b→ c)

A: from the questionoptionaa∨b→b∧c≡a+b'+bc=a'b'+b+c not…

Q: Prove that the following wff is a tautology, a contradiction or neither. Be sure to say which one.…

A: Tautology: A tautology is a statement that is always true, no matter what the circumstance. It is a…

Q: (a) Vx (P(x)→ Q(x)) → (3x P(x)→→ 3x Q(x)) ((x)0 XA (x)d XA) ((x)0 (x)d) XE (9) (c) 3x (P(x) → Q(x))…

Q: Let W1, W2, W be wffs in Propositional Logic. (i) Prove that W1, W2 = W A F (Wi→ (W2 → W)). (ii)…

A: Let be WFFs in Propositional Logic. Now,…

Q: Use truth tables to prove the following distributive properties for propositional logic. (a) p ∧ (q…

A: Is p ∧ (q ∨ r) logically equivalent to (p ∧ q) ∨ (p ∧ r)? p q r p∧q p∧r (p∧q)∨ (p∧r)…

Q: The following two sentences of TFL are not equivalent. (R → ¬ T); (¬ R ∧ T) (a) Determine what…

A: The Given two sentence are : R ->¬T ; ¬R∧T A) we are going to use truth table to show that the…

Q: Faulty logic? Is this boolean equation valid or invalid for all possible values of x,y and z? x XOR…

Q: Complete the logical proof for the following argument. ExP(x) X(P(x) → Q(x)) : 3xQ(x) Justification…

A: Here we have given 2 premises and one conclusion in predicate calculus. Premise 1 ∃x P(x) There…

Q: 6. Prove or disprove that the two propositions in each pair are equivalent. a) (p→ (q → r)),…

A: Task : Given the expression. The task is to check if these expression are equal or not.

Q: Show the following: (a) p ∧ t ≡ p, where t is a tautology. (b) p ∧ c ≡ c, where c is a…

A: A tautology is assertion that is always true for all possible chances. A contradiction is an…

Q: use propositional logic to see if the argument is valid (A ∧ B) ∧ (B → A’) → (C ∧ B’) A ∧ B…

A: Here in this question we have given a logical statement and we have asked to show that this is valid…

Q: Thank you. I can see that you have now applied De Morgan's the same way I do (I'm still confused as…

A: Boolean algebra is a fundamental branch of mathematics used in digital logic and computer science to…

Q: Consider the following premises: 1. A (B A) is a Theorem of Propositional Calculus/Logic…

A: the answer is given below:-

Q: Write the following in disjunctive normal form using logical equivalences ( p ∨q) →(p ∧¬r).

A: A Disjunctive normal form is the way of expressing the expression as disjunction of conjunctions A…

Q: table to determine if the following pairs of expressions are logical tautologies.…

A: Use a truth table to determine if the following pairs of expressions are logical tautologies.…

Q: r) and (p ∨ q) ∧ (p ∨ r) are logically equivalent. This is the distributive law of disjunction over…

A: Sorry for that as per the bartleby guidelines we can solve only one question for you if you want…

Q: use propositional logic to prove that the argument is valid. do not use truth tables…

A: argument is: (¬Av¬B→C∧D)∧¬D∴B

Q: Show that (p ∧ q) → r and (p → r) ∧ (q → r) are not logically equivalent, without using truth tables

A: In step 2, I have provided brief answer of the given question--------------

Q: Consider the first-order logic formula 3x P(a,x)→→y P(b, y) and the interpretation domain D = {1, 2,…

A: Here the variable x and y is used with existential quantifier. It means the statement should hold…

Q: Simplify the following logic formulas. Use a truth table to show that your simplification is…

A: (a) (p∧q)∨q The simplification of the logic formula is: (p∧q)∨q (p∨q)∧(q∨q) =q

Q: Use propositional logic to prove the argument valid: (P∨(Q∧R))∧(R'∨S)∧(S→T')→(T→P)

A: An argument is valid if and only if the result in the tautology becomes 1 after solving the given…

Concept explainers

Intelligent Machines

Machines that use artificial intelligence to learn from the environment and past experiences to perform better in the presence of variability and uncertainty are called intelligent machines. Intelligence develops according to environment and experience. It is human-like behavior. When the computer system or any programmed machine learns from the inputs and corresponding outputs, it can be called an intelligent machine.

Question

Given the following premises:
(1) Vx (A(x)→ B(x))
(2) Vx (B(x)→ C(x))
Prove the conclusion Vx (A(x) →→ C(x)) using the rules of first-order logic.
Show your step-by-step reasoning.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

VIEW

Step 2: Proof

VIEW

Solution

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

Given interpretations (a) (Vx) (y) P(x, y) → (x)(Vy) P(x, y) (b) (Vx) [P(x) → Q(x)] → [(x) P(x) → (Vx)Q(x)] (c) (Vx)[A(x)]' → [(Vx)A(x)]' to prove that each of the following wffs is not valid.
Use propositional logic to prove that the argument is valid. (A→(B ∨ C))∧¬C→(A→B)
Use the laws of propositional logic (logical equivalences) to show the following equivalency by choosing to change one, and only one, side of the equivalence expression. (¬p→q)∨¬q ≡ T
Given the following premises: (1) ∀x (R(x) → S(x))(2) ¬S(c) Use modus tollens to derive the conclusion ¬R(c). Show your step-by-step reasoning.
Let P(x) and Q(x) be relations, with x a variable from a given domain of discourse U. The Axiom of the Hilbert deductive system for first-order logic applied below is "Axiom 1,2,3,4,5" ? ⊢ ∀x P(x) → (∃x Q(x) → ∀x P(x)) Consider the steps given below of a proof in the Hilbert deductive system and determine the reason that justifies each. ∀x A(x) ⊢ ∀x A(x) "?"∀x A(x) ⊢ ∀x A(x) → A(a) " ?"∀x A(x) ⊢ A(a) " ?"
Show that the following two formulas are NOT logically equivalent by giving a model in which one is true and the other is false: ∃x ( R(x) → S(x) ) and ¬ ∀x ( R(x) ∧ S(x) )
3. Prove ⊢ (¬A → A) → A in Hilbert deductive system. Note: In addition to the axioms and rule of inference of H, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook). You may not use theorem 3.31, as this is precisely that theorem.Theorem 3.20 ⊢ ¬A → (A → B). Theorem 3.21 ⊢ A → (¬A → B). Theorem 3.22 ⊢ ¬¬A → A. Theorem3.23 ⊢A→¬¬A.Theorem3.25 ⊢(A→B)→(¬B→¬A).Theorem3.28 ⊢(¬A→false)→A.Rule 3.29 (Reductio ad absurdum) Theorem3.30 ⊢(A→¬A)→¬A. Prove {¬A} ⊢ (¬B → A) → B in H. Note: In addition to the axioms and rule of inference of Hilbert deductive system, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook).
Use Conditional Proofs (CP) to show that each of the following symbolic arguments are valid. Commas mark the breaks between premises. P→(Q→R) ∴ Q→(P→R) P→Q ∴ P→(Q v R) (B∙D)→(C∙R), D ∴ B→R (Z∙~W)→(X∙U), Z→(W→Y) ∴ Z→(~Y→U) (E∨F)→G, A→[(B v C)→(D∙E)] ∴ A→(C→G)
Determine whether or not the following statement is a tautology or not and give reasoning. If you need to, you can build a truth table to answer this question. (q→p)∨(∼q→∼p) A. This is a tautology because it is always true for all truth values of p and q. B. This is not a tautology because it is always false for all truth values of p and q. C. This is a tautology because it is not always false for all values of p and q. D. This is not a tautology becasue it is not always true for all truth values of p and q.
The following sentence is a theorem of truth functional logic. (P → (Q → (P ∧ Q))) (a) Explain in a sentence how to use a natural deduction proof to show that a sentence of TFL is a theorem (1 point). (b) Using any of the proof rules (from Ch. 16 & 18 of the text) in the natural deduction system, complete a proof that shows that this sentence is a theorem
Problem 1. Use the Boolean algebra derivation (instead of truth table) to prove or answer the questions. p↔q = (p→q)^ (q→→p) pvq-(p→q) →q (p+q)' =p' q Is ((p = q)) ((pr) ➡(qr)) a tautology, why? Provide the proof or disproof. Is (p q) (p →q) a tautology, why? Provide the proof or disproof.
Simplify the following logic formulas. Use a truth table to show that your simplification is correct. (a.) (p∧q)∨q(p∧q)∨q (b.) p→(p→q)p→(p→q) (c.) ¬(¬p∧¬q)¬(¬p∧¬q) "Simplify" means: find the simplest/smallest formula that means the same thing.