1. Construct the truth table for the following logical expression.a) p+¬(r ^ (p→q))(Arvs(ArvalQveb) State whether it is a tautology, contingency or contradiction.

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Answered: 1. Construct the truth table for the…

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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1. With the aid of Truth tables, determine which of the following logical statements (or expressions)is a Tautology, a Contradiction, or a Contingency.(a) (p ↔ q) ↔ ((p → q) ∧ (q → p))(b) (p → (q → r)) ↔ (p ∧ q → r)(c) (p → r ∨ q)⊕(q ∧ r)(d) p ∨ q ∧ (¬r → ¬p ∧ ¬q) 2. With reference to the following logical equivalences, determine whether each of them is valid orinvalid. If it is invalid then give a counterexample (e.g. based on a Truth-Value assignment).If it is valid then give an algebraic proof using ONLY logical equivalences from Table 6 inSection 1.3 of course textbook, and the rule for conditional: p → q ≡ ¬p ∨ q.(a) p → (q → r) ≡ (p → q) → r(b) (p → r) ∨ (q → r) ≡ (p ∧ q) → r(c) (¬p → (q ∧ ¬q)) ≡ p(d) p ∧ q → r ≡ (¬p ∧ ¬q) → ¬r 3. Express the following logical statements in terms of the Contrapositive, Converse, and Inverse,respectively.(a) You are an adult provided that you are above 18 years of age.(b) It is daylight whenever the sun is shining.(c) 3 × 2 = 6 only if 2 × 3 = 6.

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1. Construct the truth table for the following logical expression. a) p+-(r^ (p → q)) (ArvalQve b) State whether it is a tautology, contingency or contradiction.