Question

If I=[a,b] and I'=[a',b'] are closed intervals in R, prove that I ⊆ I' if and only if a'≤a and b≤b'.

Name: if iab and iab are closed intervals in r prove that i i if and only if aa and bb
Uploaded: 2023-05-23T22:20:12-08:00
Duration: 1 min 46 s
Channel: Hoan Nguyen
Description: if iab and iab are closed intervals in r prove that i i if and only if aa and bb

          If I=[a,b] and I'=[a',b'] are closed intervals in R, prove that I ⊆ I' if and only if a'≤a and b≤b'.

Added by Valentina G.

Calculus: One Variable

Garret J. Etgen, Saturnino L. Salas 10th Edition

Chapter 1

Instant Answer

Solved by Expert Hoan Nguyen

05/23/2023

Step 1

Assume that a'≤a and b≤b'. We want to show that for any x in I, x is also in I'. Since x is in I, we have a≤x≤b. Now, since a'≤a, we have a'≤x. Similarly, since x≤b and b≤b', we have x≤b'. Show more…

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