For each of the following pairs of statements, determine whether two statements are equivalent or not. 1. For all integers x>20, for all integers y>30, sin(x) * cos(y) > 1/(xy). For all integers y>30, for all integers x>20, sin(x) * cos(y) > 1/(xy). 2. There exists an integer x>0 so that for all integers y>0, we have xy=2y. For all integers y>0, there exists an integer x>0 so that xy=2y.
For each of the following pairs of statements, determine whether two statements are equivalent or not. 1. For all integers x>20, for all integers y>30, sin(x) * cos(y) > 1/(xy). For all integers y>30, for all integers x>20, sin(x) * cos(y) > 1/(xy). 2. There exists an integer x>0 so that for all integers y>0, we have xy=2y. For all integers y>0, there exists an integer x>0 so that xy=2y.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 4E
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For each of the following pairs of statements, determine whether two statements are equivalent or not.
1.
For all integers x>20, for all integers y>30, sin(x) * cos(y) > 1/(xy).
For all integers y>30, for all integers x>20, sin(x) * cos(y) > 1/(xy).
2.
There exists an integer x>0 so that for all integers y>0, we have xy=2y.
For all integers y>0, there exists an integer x>0 so that xy=2y.
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