If H = { x E R | sin x = 0 }, then H is finite. If E = { x €Z| 2x2 +x -1 = 0 }, then |E| = 2. If K = { XENI IX – 31 < 10} then K is infinite -

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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Topic: Sets and Basic Notations

Directions:

The following statements are FALSE. Give a proper reasoning or exhibit a
counterexample to emphasize its falsity.

1. If F = { x € Q | x² +1 = 0 }, then |F| = 2.
2. If H = { x ER| sin x = 0 }, then H is finite.
3. If E = { x € Z | 2x? + x – 1 = 0 }, then |E| = 2.
4. If K = { x EN| |x - 3| < 10 }, then K is infinite.
5. Let T = { x ER | x² +4 >0}. Then, T CR.
6. Let V = { x EZ |x* –
%3D
%3D
%3D
9x2 + 20 = 0 }. Then, |P(V)| = 16.
-
%3D
Transcribed Image Text:1. If F = { x € Q | x² +1 = 0 }, then |F| = 2. 2. If H = { x ER| sin x = 0 }, then H is finite. 3. If E = { x € Z | 2x? + x – 1 = 0 }, then |E| = 2. 4. If K = { x EN| |x - 3| < 10 }, then K is infinite. 5. Let T = { x ER | x² +4 >0}. Then, T CR. 6. Let V = { x EZ |x* – %3D %3D %3D 9x2 + 20 = 0 }. Then, |P(V)| = 16. - %3D
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