1. Consider the following statements: P(x, y) = "3r ER such that Vy ER, x+y=0" Q(x, y) = "Vr Ry R such that z+y=0" Explain the difference between what these two statements are claiming. Which of them is true and which of them is false?
1. Consider the following statements: P(x, y) = "3r ER such that Vy ER, x+y=0" Q(x, y) = "Vr Ry R such that z+y=0" Explain the difference between what these two statements are claiming. Which of them is true and which of them is false?
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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Question
Transcribed Image Text:1. Consider the following statements:
R such that Vy € R, zx+y=0"
P(x, y) = "
Q(x, y) = "Vr
Ry R such that x+y=0"
Explain the difference between what these two statements are claiming. Which of them is true and which
of them is false?
Expert Solution
Step 1
Here, P(x,y) ="∃x ∈ R such that ∀y ∈ R, x + y = 0"
- There exists some value of x for every value of y such that x+y = 0
- Take some input y∈R, then we can have x = -y ∈R.
- This statement is true.
∴ x+y = 0
and Q(x,y) ="∀x ∈ R ∃y ∈ R such that, x + y = 0"
- For every value of x, there exists some value of y such that x+y = 0
- Take some input x∈R, then we can have y = -x ∈R.
- This statement is true.
∴ x+y = 0
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