a) Show that: (Vx) (A → (B = C)) → ((Vx)(A → B) = (Vx)(A → C))←b) Show that:(\x)((A v B) → C) → (Vx) (A → C)c) [Show that:(Vx)(A → (B ^ C)) → (Vx)(A → B)d) Prove (A V (Vx) BC = (Vx) B(A V C), as long as x not free in A. (Hint: Translate first to Standardnotation)

Given: ∀x(A→(B≡C))→(∀x(A→B)≡∀x(A→C)) Prove: ∀x(A→B)≡∀x(A→C) Assume ∀x(A→B). Then, for any a,…

(Vx) (A → (B = C)) → ((Vx) (A → B) = (Vx) (A → C)) - a) Show that: b) Show that: (Vx) ((A v B) → C) → (Vx)(A → C) c) [Show that: (Vx)(A → (BAC)) → (Vx) (A → B) d) Prove (AV (Vx) BC = (Vx) B(A V C), as long as x not free in A. (Hint: Translate first to Standard notation)

(Vx) (A → (B = C)) → ((Vx) (A → B) = (Vx) (A → C)) - a) Show that: b) Show that: (Vx) ((A v B) → C) → (Vx)(A → C) c) [Show that: (Vx)(A → (BAC)) → (Vx) (A → B) d) Prove (AV (Vx) BC = (Vx) B(A V C), as long as x not free in A. (Hint: Translate first to Standard notation)

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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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

a) Show that: (Vx) (A → (B = C)) → ((Vx)(A → B) = (Vx)(A → C))
←
b) Show that:
(\x)((A v B) → C) → (Vx) (A → C)
c) [Show that:
(Vx)(A → (B ^ C)) → (Vx)(A → B)
d) Prove (A V (Vx) BC = (Vx) B(A V C), as long as x not free in A. (Hint: Translate first to Standard
notation)

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need help finding the logic expressions for these 4 k maps
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