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Replaung A wih AVB, we may assume A and B are disjint (smre AvB: (AiB) UB) If A-0, then AVB = B is denumermble If A # P, Since A is fomite, we can write A fai, a. on 3 for some n Zt Simce B is denumerable, wnite we can De fime f Z+ → AUB ak A- fai, as. , on3 B = ... f:Z+ → AVB

Replaung A wih AVB, we may assume A and B are disjint (smre AvB: (AiB) UB) If A-0, then AVB = B is denumermble If A # P, Since A is fomite, we can write A fai, a. on 3 for some n Zt Simce B is denumerable, wnite we can De fime f Z+ → AUB ak A- fai, as. , on3 B = ... f:Z+ → AVB

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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Please complete this. I do not know how to show the identity to prove bijection
Replaung A wth AlB, we may assume A and B are disjrint (smce AUB= (A IB) VB) If A-0, then AVB = B is denumermble If A #P, Since A is fonite, we can write an3 for some n6 Zt Simce B is denumerable , we can write B = De fime f:Z+ → AUB ak , Isken bixn A- fa, a. f:Z+ → AVB ak Isken bian ntl <K De fime X= ai tA x = bi eB Show f and inver ses ore fog identity functins are got Note is well-defined since ANB= 0
Transcribed Image Text:Replaung A wth AlB, we may assume A and B are disjrint (smce AUB= (A IB) VB) If A-0, then AVB = B is denumermble If A #P, Since A is fonite, we can write an3 for some n6 Zt Simce B is denumerable , we can write B = De fime f:Z+ → AUB ak , Isken bixn A- fa, a. f:Z+ → AVB ak Isken bian ntl <K De fime X= ai tA x = bi eB Show f and inver ses ore fog identity functins are got Note is well-defined since ANB= 0
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