Prove ¬(3x € X : (Vy ¤ Y : E(x, y))) = \x € X : (‡y ¤ Y : ¬E(x,y)) (Vx X: (³y € Y : E(x, y))) = (3x € X : (Vy ≤ Y : ¬E(x, y))) ¬(3x € X : ¬E(x)) = (Vx ≤ X : E(x))

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 20E
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Prove
¬(3x € X : (Vy ≤ Y : E(x, y))) = \x ≤ X : (³y ≤Y : ¬E(x, y))
(Vx X: (y € Y : E(x, y))) = (3x € X : (Vy ≤ Y : ¬E(x, y)))
(3x € X: ¬E(x)) = (Vx X: E(x))
Transcribed Image Text:Prove ¬(3x € X : (Vy ≤ Y : E(x, y))) = \x ≤ X : (³y ≤Y : ¬E(x, y)) (Vx X: (y € Y : E(x, y))) = (3x € X : (Vy ≤ Y : ¬E(x, y))) (3x € X: ¬E(x)) = (Vx X: E(x))
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