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截屏: 3. Decide whether the following statements are true or false. If they are true, prove them; if they are false, provide a counterexample (and show that it is indeed a counterexample). (a) The addition of two rational numbers is rational. (b) The addition of two irrational numbers is irrational. (c) Every equation of the form ax² + bx + c = 0 where a, b, c Є Z has a real number solution. (d) IF a b and b | 15, THEN a | (45 +262 - 7ab). (e) log2 (3) is a rational number.

截屏: 3. Decide whether the following statements are true or false. If they are true, prove them; if they are false, provide a counterexample (and show that it is indeed a counterexample). (a) The addition of two rational numbers is rational. (b) The addition of two irrational numbers is irrational. (c) Every equation of the form ax² + bx + c = 0 where a, b, c Є Z has a real number solution. (d) IF a b and b | 15, THEN a | (45 +262 - 7ab). (e) log2 (3) is a rational number.

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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截屏: 3. Decide whether the following statements are true or false. If they are true, prove them; if they are false, provide a counterexample (and show that it is indeed a counterexample). (a) The addition of two rational numbers is rational. (b) The addition of two irrational numbers is irrational. (c) Every equation of the form ax² + bx + c = 0 where a, b, c Є Z has a real number solution. (d) IF a b and b | 15, THEN a | (45 +262 - 7ab). (e) log2 (3) is a rational number.
Transcribed Image Text:截屏: 3. Decide whether the following statements are true or false. If they are true, prove them; if they are false, provide a counterexample (and show that it is indeed a counterexample). (a) The addition of two rational numbers is rational. (b) The addition of two irrational numbers is irrational. (c) Every equation of the form ax² + bx + c = 0 where a, b, c Є Z has a real number solution. (d) IF a b and b | 15, THEN a | (45 +262 - 7ab). (e) log2 (3) is a rational number.
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