7. Negate the statement "For every a, b e R with a < b there is an r € Q with a 0 there is an n E N such that | sin n < ɛ. 9. Negate the statement "For every x E R there is an n EN such that x < n." 10. Negate the statement "There is an a E R such that for every ɛ > 0 there is a KeN such that for every n EN with n > K we have |(1+1/n)" – a| < E."

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Discrete mathematics short question

Topic: (Quantifiers)

7. Negate the statement "For every a, b e R with a < b there is an r € Q
with a <r < b.
8. Negate the statement "For every e > 0 there is an n E N such that
| sin n| < ɛ.
9. Negate the statement "For every x E R there is an n EN such that x < n."
10. Negate the statement "There is an a e R such that for every & > 0 there is
a KeN such that for every n EN with n > K we have |(1+1/n)" – a| <
E."
Transcribed Image Text:7. Negate the statement "For every a, b e R with a < b there is an r € Q with a <r < b. 8. Negate the statement "For every e > 0 there is an n E N such that | sin n| < ɛ. 9. Negate the statement "For every x E R there is an n EN such that x < n." 10. Negate the statement "There is an a e R such that for every & > 0 there is a KeN such that for every n EN with n > K we have |(1+1/n)" – a| < E."
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