Let D = E = {−2, −1, 0, 1, 2}. Write negations for each of the following statements and determine which is true, the given statement or its negation. (a) ∀x in D, ∃y in E such that x + y = 1. Negation: in D such that in E, x + y 1. The given statement is true. The negation is true. (b) ∃x in D such that ∀y in E, x + y = −y. Negation: in D, in E such that x + y −y. The given statement is true. The negation is true. (c) ∀x in D, ∃y in E such that xy ≥ y. Negation: in D such that in E, xy y. The given statement is true. The negation is true. (d) ∃x in D such that ∀y in E, x ≤ y. Negation: in D, in E such that x y. The given statement is true. The negation is true.
Let D = E = {−2, −1, 0, 1, 2}. Write negations for each of the following statements and determine which is true, the given statement or its negation. (a) ∀x in D, ∃y in E such that x + y = 1. Negation: in D such that in E, x + y 1. The given statement is true. The negation is true. (b) ∃x in D such that ∀y in E, x + y = −y. Negation: in D, in E such that x + y −y. The given statement is true. The negation is true. (c) ∀x in D, ∃y in E such that xy ≥ y. Negation: in D such that in E, xy y. The given statement is true. The negation is true. (d) ∃x in D such that ∀y in E, x ≤ y. Negation: in D, in E such that x y. The given statement is true. The negation is true.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let
D = E = {−2, −1, 0, 1, 2}.
Write negations for each of the following statements and determine which is true, the given statement or its negation.(a)
∀x in D, ∃y in E such that
x + y = 1.
Negation:
in D such that in
E, x + y
1.
The given statement is true. The negation is true.
(b)
∃x in D such that ∀y in E,
x + y = −y.
Negation:
in D, in E such that
x + y
−y.
The given statement is true. The negation is true.
(c)
∀x in D, ∃y in E such that
xy ≥ y.
Negation:
in D such that in
E, xy
y.
The given statement is true. The negation is true.
(d)
∃x in D such that ∀y in E,
x ≤ y.
Negation:
in D, in E such that
x
y.
The given statement is true. The negation is true.
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