Here is a statement and a proof for it. Read it carefully and select the correct answer below, giving a short explanation, if applicable. STATEMENT. Let x and y be real numbers such that their product ay is rational. Then x and y are rational themselves. PROOF. For x and y to be rational means that there are a, b, c, d E Z with b 0 and d 0 such that x = and y = . Then xy = is rational, since ac € Z and bd € Z with bd 0. Since ay is given to be rational it follows that x and y are rational. The statement is correct and the proof is sound. The statement is correct but the proof is not sound since [fill in the box below] The statement is false and the proof is erroneous since [fill in the box below] None of the above ONot answered Briefly state your reasoning here:
Here is a statement and a proof for it. Read it carefully and select the correct answer below, giving a short explanation, if applicable. STATEMENT. Let x and y be real numbers such that their product ay is rational. Then x and y are rational themselves. PROOF. For x and y to be rational means that there are a, b, c, d E Z with b 0 and d 0 such that x = and y = . Then xy = is rational, since ac € Z and bd € Z with bd 0. Since ay is given to be rational it follows that x and y are rational. The statement is correct and the proof is sound. The statement is correct but the proof is not sound since [fill in the box below] The statement is false and the proof is erroneous since [fill in the box below] None of the above ONot answered Briefly state your reasoning here:
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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![Here is a statement and a proof for it. Read it carefully and select the correct answer below, giving a short
explanation, if applicable.
STATEMENT. Let x and y be real numbers such that their product xy is rational. Then x and y are
rational themselves.
PROOF. For x and y to be rational means that there are a, b, c, d ≤ Z with b ‡ 0 and d ‡ 0 such that
X = and y = . Then xy acis rational, since ac € Z and bd € Z with bd ‡ 0. Since xy is given to be
rational it follows that x and y are rational.
bd
=
The statement is correct and the proof is sound.
The statement is correct but the proof is not sound since [fill in the box below]
The statement is false and the proof is erroneous since [fill in the box below]
None of the above
ONot answered
Briefly state your reasoning here:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea7bbfe4-f0d9-4343-839c-f9e5c129de8e%2F048a8bc1-71bb-416c-a840-198f21091b26%2F4lbjnx8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Here is a statement and a proof for it. Read it carefully and select the correct answer below, giving a short
explanation, if applicable.
STATEMENT. Let x and y be real numbers such that their product xy is rational. Then x and y are
rational themselves.
PROOF. For x and y to be rational means that there are a, b, c, d ≤ Z with b ‡ 0 and d ‡ 0 such that
X = and y = . Then xy acis rational, since ac € Z and bd € Z with bd ‡ 0. Since xy is given to be
rational it follows that x and y are rational.
bd
=
The statement is correct and the proof is sound.
The statement is correct but the proof is not sound since [fill in the box below]
The statement is false and the proof is erroneous since [fill in the box below]
None of the above
ONot answered
Briefly state your reasoning here:
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