6. Use rules of inference to show that if Vr(P(x) v Q(x)) and Vr((-P(x) ^ Q(x)) → R(x)) aretrue, then Vx(-R(x) → P(x)) is also true, where the domains of all quantifiers are the same.7. (a) Prove that m³ + 2n² = 36 has no solution in positive integers.(b) Prove that for every n e Z, n³ +n is even.(c) Prove that for all n e Z, n is odd if and only if n + 2 is odd.(d) Prove that the product of two consecutive integers is even.

Given,Use rules of inference to show that if ∀x(P(x) v Q(x)) and ∀r((~P(x) ^ Q(x)) → R(x)) are true,…

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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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6. Use rules of inference to show that if Vr(P(x) v Q(x)) and Vr((-P(x) ^ Q(x)) → R(x)) are
true, then Vx(-R(x) → P(x)) is also true, where the domains of all quantifiers are the same.
7. (a) Prove that m³ + 2n² = 36 has no solution in positive integers.
(b) Prove that for every n e Z, n³ +n is even.
(c) Prove that for all n e Z, n is odd if and only if n + 2 is odd.
(d) Prove that the product of two consecutive integers is even.

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Use rules of inference to show that if ∀x(P(x) v Q(x)) and ∀r((~P(x) ^ Q(x)) → R(x)) are true, then ∀x(~R(x) → P(x)) is also true, where the domains of all quantifiers are the same.

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