2. With reference to the following logical equivalences, determine whether each of them is valid or invalid. 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 in Section 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
2. With reference to the following logical equivalences, determine whether each of them is valid or invalid. 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 in Section 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
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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2. With reference to the following logical equivalences, determine whether each of them is valid or
invalid. 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 in
Section 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
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