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1.7. (-) The statement below is not always true for x, y e R. Give an example where it is false, and add a hypothesis on y that makes it a true statement. "If x and y are nonzero real numbers and x > y, then (−1/x) > (-1/y)."

1.7. (-) The statement below is not always true for x, y e R. Give an example where it is false, and add a hypothesis on y that makes it a true statement. "If x and y are nonzero real numbers and x > y, then (−1/x) > (-1/y)."

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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1.7. (-) The statement below is not always true for x, y e R. Give an example where it is false, and add a hypothesis on y that makes it a true statement. "If x and y are nonzero real numbers and x > y, then (−1/x) > (−1/y).”
Transcribed Image Text:1.7. (-) The statement below is not always true for x, y e R. Give an example where it is false, and add a hypothesis on y that makes it a true statement. "If x and y are nonzero real numbers and x > y, then (−1/x) > (−1/y).”
Expert Solution
Step 1

given that if x and y are nonzero real numbers and x>y then (-1x)>(-1y)

in the first case we give an example of given statement is false.

if  x = 3 and y = -1 where x>y 

then -1x=-13 and -1y=1

but (-1x=-0.33)<(-1y=1)

therefore (-1x)<(-1y)

here we have proved that the given statement is false for x = 3 and y=-1

 

 

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