2. Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. If true, give a brief explanation for why. If false, give a counterexample (i.e. a set of values x,y that make the statement false. You must also explain why they make the statement false.) a) ³yVx((y > x²) → y > x) b) Vy!x(√√y < 0) c) ³xVy((√x + y²) → (x > 0)) d) xy(>0Vx<0⇒x ≥y) exy(x² = y² ↔ y³ = x³)

2. Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. If true, give a brief explanation for why. If false, give a counterexample (i.e. a set of values x,y that make the statement false. You must also explain why they make the statement false.) a) ³yVx((y > x²) → y > x) b) Vy!x(√√y < 0) c) ³xVy((√x + y²) → (x > 0)) d) xy(>0Vx<0⇒x ≥y) exy(x² = y² ↔ y³ = x³)

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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Intelligent Machines

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

2. Determine the truth value of each of these statements if the domain of
each variable consists of all real numbers. If true, give a brief explanation
for why. If false, give a counterexample (i.e. a set of values x,y that make
the statement false. You must also explain why they make the statement
false.)
a) yvx((y > x²) → y > x)
b) Vy!x(√√ < 0)
c) xy((√√x y²) → (x > 0))
d) x(x < 0⇒x² ≥y)
e) \xy(x² = y² ↔ y³ = x³)

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