1. Consider the following statements: P(x, y) = "3r ER such that Vy R, z+y=0" Q(x, y) ="Vr Ry R such that x+y=0"

C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter6: Modularity Using Functions
Section6.5: Variable Scope
Problem 4E
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1. Consider the following statements:

\( P(x, y) = \exists x \in \mathbb{R} \) such that \( \forall y \in \mathbb{R}, \, x + y = 0 \)

\( Q(x, y) = \forall x \in \mathbb{R} \, \exists y \in \mathbb{R} \) 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?
Transcribed Image Text:1. Consider the following statements: \( P(x, y) = \exists x \in \mathbb{R} \) such that \( \forall y \in \mathbb{R}, \, x + y = 0 \) \( Q(x, y) = \forall x \in \mathbb{R} \, \exists y \in \mathbb{R} \) 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

R:

R means Real numbers.

Real numbers includes both rational numbers and irrational numbers.

Example of real numbers: 4,-5, 22/7, and so on.

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