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6. For A, B C R, define A + B = {a+b: a € A, b € B} A B = {a -b: a € A, b E B} %3D (i) Determine {3, 1,0} + {2,0, 2, 1} and {3, 1,0} {2,0, 2, 1}

6. For A, B C R, define A + B = {a+b: a € A, b € B} A B = {a -b: a € A, b E B} %3D (i) Determine {3, 1,0} + {2,0, 2, 1} and {3, 1,0} {2,0, 2, 1}

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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Problem 6. (i) please!
inf(A) = -sup(-A) 4. Let A = {, ne N}. Prove that sup(A) = 1, inf(A) = . 5. (i) Let A, BCR be sets which are bounded above, such that A C B. Show that sup(A) < sup (ii) Let A, BCR such that sup(A) < sup(B). Show that there exists b E B that is an upper b0 Show that this result does not hold if we instead assume that sup(A) < sup(B). 6. For A, B CR, define A + B = {a+b:a E A, b E B} A·B = {a -b: a E A, b E B} (i) Determine {3, 1,0} + {2,0, 2, 1} and {3, 1,0} {2,0, 2, 1} (ii) Assume that sup(A) and sup(B) exist. Prove that sup(A+ B) = sup(A) + sup(B). (iii) Give an example of sets A, B where sup(A B) + sup(A) - sup(B) !! Warm-up Problems, Not for credit: 1. Let F be any field. Prove that both the additive and multiplicative identities in F are unique. 2. Given an ordered field F, we saw that it has a set of positive elements P satisfying certain two 입력하십시오. LG
Transcribed Image Text:inf(A) = -sup(-A) 4. Let A = {, ne N}. Prove that sup(A) = 1, inf(A) = . 5. (i) Let A, BCR be sets which are bounded above, such that A C B. Show that sup(A) < sup (ii) Let A, BCR such that sup(A) < sup(B). Show that there exists b E B that is an upper b0 Show that this result does not hold if we instead assume that sup(A) < sup(B). 6. For A, B CR, define A + B = {a+b:a E A, b E B} A·B = {a -b: a E A, b E B} (i) Determine {3, 1,0} + {2,0, 2, 1} and {3, 1,0} {2,0, 2, 1} (ii) Assume that sup(A) and sup(B) exist. Prove that sup(A+ B) = sup(A) + sup(B). (iii) Give an example of sets A, B where sup(A B) + sup(A) - sup(B) !! Warm-up Problems, Not for credit: 1. Let F be any field. Prove that both the additive and multiplicative identities in F are unique. 2. Given an ordered field F, we saw that it has a set of positive elements P satisfying certain two 입력하십시오. LG
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