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6. Determine whether each of the following statements is true or false. If the statement is true, then prove it. If the statement is false, write down the negation of the statement and prove that. (a) x E R, 3y E R, x + y > 0. (b) Vx E R, 3y E R, x – y > 0. (c) 3x E R, Vy E R, x + y > 0. (d) Vr E R, 3y E R, xy > 0.

6. Determine whether each of the following statements is true or false. If the statement is true, then prove it. If the statement is false, write down the negation of the statement and prove that. (a) x E R, 3y E R, x + y > 0. (b) Vx E R, 3y E R, x – y > 0. (c) 3x E R, Vy E R, x + y > 0. (d) Vr E R, 3y E R, xy > 0.

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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6. Determine whether each of the following statements is true or false. If the statement is true, then prove it. If the statement is false, write down the negation of the statement and prove that. (a) Vx E R, 3y E R, x + y > 0. (b) Vx E R, 3y E R, x – y > 0. (c) 3x E R, Vy E R, x + y > 0. (d) Vx E R, 3y E R, xy > 0. (e) 3x ER, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0. (h) Vx E R, 3y E R, (x + y > 0 or x + y = 0). (i) Vx E R, 3y E R, (x + y > 0 and x +y = 0). (j) (Vx E R, 3y E R, x + y > 0) and (Vx E R, 3y E R, x + y = 0).
Transcribed Image Text:6. Determine whether each of the following statements is true or false. If the statement is true, then prove it. If the statement is false, write down the negation of the statement and prove that. (a) Vx E R, 3y E R, x + y > 0. (b) Vx E R, 3y E R, x – y > 0. (c) 3x E R, Vy E R, x + y > 0. (d) Vx E R, 3y E R, xy > 0. (e) 3x ER, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0. (h) Vx E R, 3y E R, (x + y > 0 or x + y = 0). (i) Vx E R, 3y E R, (x + y > 0 and x +y = 0). (j) (Vx E R, 3y E R, x + y > 0) and (Vx E R, 3y E R, x + y = 0).
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