Analyze the argument and its translation in quantificational logic: "All humans are mortals. Socrates is human. Therefore, Socrates is mortal. " [Hx, Mx] 1. (x) (Hx Ɔ Mx) Valid 2. Hs .. Ms 3. asm: ~ Ms 4. (Hs ɔ Ms) {from 1} 5. Ms {from 4 and 2}MP {Line 3 and 5 Contradicts} What rule was used in obtaining line 4? A) Drop Universal Modus Ponens Reverse Squiggle D) Drop Existential

Analyze the argument and its translation in quantificational logic: "All humans are mortals. Socrates is human. Therefore, Socrates is mortal. " [Hx, Mx] 1. (x) (Hx Ɔ Mx) Valid 2. Hs .. Ms 3. asm: ~ Ms 4. (Hs ɔ Ms) {from 1} 5. Ms {from 4 and 2}MP {Line 3 and 5 Contradicts} What rule was used in obtaining line 4? A) Drop Universal Modus Ponens Reverse Squiggle D) Drop Existential

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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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
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Consider the wffs:φ1 ≡ p1 → (p2 → (p3 → p4))φ2 ≡ (p1 ∧ p2 ∧ p3) → p4(a) Technically speaking, neither φ1 nor φ2 is well-formed since neither is allowed by the formal syntaxof propositional logic. Correct them. Note, however, that we will freely make such trivial ’errors’ throughout this semester (as do most such courses).(b) Use truth tables (in the form defined in this course) to show that φ1 ↔ φ2.(c) After internalizing an intuitive understanding of this equality, propose an extension of it to n atoms.(d) State the number of rows in a truth table for proving the extension
Consider the wffs:φ1 ≡ p1 → (p2 → (p3 → p4))φ2 ≡ (p1 ∧ p2 ∧ p3) → p4(a) Technically speaking, neither φ1 nor φ2 is well-formed since neither is allowed by the formal syntaxof propositional logic. Correct them. Note, however, that we will freely make such trivial ’errors’throughout this semester (as do most such courses).(b) Use truth tables (in the form defined in this course) to show that φ1 ↔ φ2.(c) After internalizing an intuitive understanding of this equality, propose an extension of it to natoms.(d) State the number of rows in a truth table for proving the extension.
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