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id I prove this qa is not to zero correctly? Please look over my proof and qa is not equa

id I prove this qa is not to zero correctly? Please look over my proof and qa is not equa

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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Did I prove this qa is not to zero correctly? Please look over my proof and qa is not equal to zero by what?
13. Let s be the statements : The product of nón - zero rational number irrational number and any is irrational , any a ) Write a negation for S: There exists an irrationa number and rational number a non zerO whose product is rational. 6) Prove s by contracton: Suppose not . Then there exists an irrational x and non zero rational number such that the a product of -f for some integer X.y is rational. Then let y: and x.y a b, pand b to and with a to by definition of ratonal. ly = X• g by substitution a #o hypothesis ( y is a non-zero ratonal number & 상 = ) %3D to a } by algeba. Pb %3D qa Now pd and ga ave integers since P ib,9 and a are integers and the integers are elosed under products. becall se both proren to be nantero. is vational which contradict the fact that x Therefore the assumption is irrational, vatiinal was wrong and .X is
Transcribed Image Text:13. Let s be the statements : The product of nón - zero rational number irrational number and any is irrational , any a ) Write a negation for S: There exists an irrationa number and rational number a non zerO whose product is rational. 6) Prove s by contracton: Suppose not . Then there exists an irrational x and non zero rational number such that the a product of -f for some integer X.y is rational. Then let y: and x.y a b, pand b to and with a to by definition of ratonal. ly = X• g by substitution a #o hypothesis ( y is a non-zero ratonal number & 상 = ) %3D to a } by algeba. Pb %3D qa Now pd and ga ave integers since P ib,9 and a are integers and the integers are elosed under products. becall se both proren to be nantero. is vational which contradict the fact that x Therefore the assumption is irrational, vatiinal was wrong and .X is
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