b. Determine whether the statement is true or false and justify your answer. Determine which of the statements in 15-19 are true and which are false. Prove each true statement directly from the definitions, and give a counterexample for each false statement. For a statement that is false, determine whether a small change would make it true. If so, make the change and prove the new statement. Follow the directions for writing proofs on page 173. 15. The product of any two rational numbers is a rational number.
b. Determine whether the statement is true or false and justify your answer. Determine which of the statements in 15-19 are true and which are false. Prove each true statement directly from the definitions, and give a counterexample for each false statement. For a statement that is false, determine whether a small change would make it true. If so, make the change and prove the new statement. Follow the directions for writing proofs on page 173. 15. The product of any two rational numbers is a rational number.
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:and a variable.
b. Determine whether the statement is true or
false and justify your answer.
Determine which of the statements in 15-19 are true
and which are false. Prove each true statement directly
from the definitions, and give a counterexample for each
false statement. For a statement that is false, determine
whether a small change would make it true. If so, make
the change and prove the new statement. Follow the
directions for writing proofs on page 173.
15. The product of any two rational numbers is a
rational number.
Copyright 2020 Cengage Learning. All Rights Reserved. May not be
Must x be rational? If so, express x as a ratio of
two integers.
* 29. Suppose a, b, and c are integers and x, y, and z are
nonzero real numbers that satisfy the following
equations:
xy
x+y
Is x rational? If
a and
<= a
XZ
x+z
4.3 DIR
= b and
yz
y+z
<= c.
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