(a) For all a, b, c e N, if abc > 27, then at least one of a, b, or c is greater than or equal to 3. (b) For all a, b, c E N, if abc < 27, then at least two of a, b, or c are less than or equal to 3. (c) For all a, b, c E N, if abc = 27, then at least one of a, b, or c is equal to 3.
(a) For all a, b, c e N, if abc > 27, then at least one of a, b, or c is greater than or equal to 3. (b) For all a, b, c E N, if abc < 27, then at least two of a, b, or c are less than or equal to 3. (c) For all a, b, c E N, if abc = 27, then at least one of a, b, or c is equal to 3.
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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Transcribed Image Text:(a) For all a, b, c € N, if abc > 27, then at least one of a, b, or c is greater than or
equal to 3.
(b) For all a, b, c € N, if abc < 27, then at least two of a, b, or c are less than or equal
to 3.
(c) For all a, b, c € N, if abc = 27, then at least one of a, b, or c is equal to 3.
Transcribed Image Text:4. Prove or disprove the following statements.
1This shows that we can find n – 1 consecutive composite numbers for any n > 2. In particular, there
can be arbitrarily large gaps between prime numbers.
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