2.4. Let A and B be sets of real numbers, let f be a function from R to R, and let P be the set of positive real numbers. Without using words of negation, for each statement below write a sentence that expresses its negation. a) For all x € A, there is a b € B such that b > x. b) There is an x € A such that, for all b € B, b > x. c) For all x, y = R, f(x) = f(y) ⇒ x = y.
2.4. Let A and B be sets of real numbers, let f be a function from R to R, and let P be the set of positive real numbers. Without using words of negation, for each statement below write a sentence that expresses its negation. a) For all x € A, there is a b € B such that b > x. b) There is an x € A such that, for all b € B, b > x. c) For all x, y = R, f(x) = f(y) ⇒ x = y.
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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![2.4. Let A and B be sets of real numbers, let f be a function from R to R, and let
P be the set of positive real numbers. Without using words of negation, for each
statement below write a sentence that expresses its negation.
a) For all x € A, there is a b € B such that b > x.
b) There is an x € A such that, for all b € B, b>x.
c) For all x, y eR, f(x) = f(y) ⇒ x = y.
d) For all be R, there is an x e R such that f(x) = b.
e) For all x, y e R and all € € P, there is a & E P such that |x - y] < 8 implies
\f(x) = f(y)] < €.
f) For all € € P, there is a & € P such that, for all x, y € R, \x − y| < 8 implies
|f(x) = f(y)] < €.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6184893-1e67-4ed8-9784-fdd0cf2ed60a%2F91d7442f-4947-4626-9e65-ab07bc0ff4d4%2F78inv2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.4. Let A and B be sets of real numbers, let f be a function from R to R, and let
P be the set of positive real numbers. Without using words of negation, for each
statement below write a sentence that expresses its negation.
a) For all x € A, there is a b € B such that b > x.
b) There is an x € A such that, for all b € B, b>x.
c) For all x, y eR, f(x) = f(y) ⇒ x = y.
d) For all be R, there is an x e R such that f(x) = b.
e) For all x, y e R and all € € P, there is a & E P such that |x - y] < 8 implies
\f(x) = f(y)] < €.
f) For all € € P, there is a & € P such that, for all x, y € R, \x − y| < 8 implies
|f(x) = f(y)] < €.
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