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1. The following statements are all false. Do not simply negate the statement. Give a counterexample or a proper reasoning to emphasize its falsity. a. Vx € Z, 5x² + 1 < 6. b. 3! x € Z s.t. 6x² – x – 1 = 0. c. 12x + 18y = 40 has integral solutions.

1. The following statements are all false. Do not simply negate the statement. Give a counterexample or a proper reasoning to emphasize its falsity. a. Vx € Z, 5x² + 1 < 6. b. 3! x € Z s.t. 6x² – x – 1 = 0. c. 12x + 18y = 40 has integral solutions.

Advanced Engineering Mathematics
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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Answer A,B and C only. Thank you

1. The following statements are all false. Do not simply negate the statement. Give a counterexample or a proper reasoning to emphasize its falsity. a. Vx € Z, 5x? +1 < 6. b. Э х€Z s.t. бх? — х — 1%3D0. c. 12x + 18y = 40 has integral solutions. a () • ) - () · C) 6. 6. 6 = 1024 d. () (G) 7 = 1024 7 е. 3 a.
Transcribed Image Text:1. The following statements are all false. Do not simply negate the statement. Give a counterexample or a proper reasoning to emphasize its falsity. a. Vx € Z, 5x? +1 < 6. b. Э х€Z s.t. бх? — х — 1%3D0. c. 12x + 18y = 40 has integral solutions. a () • ) - () · C) 6. 6. 6 = 1024 d. () (G) 7 = 1024 7 е. 3 a.
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