(1) Find the upper and lower bound of the following sets also state if the set is bounded or not (i) A = -{} (ii) B = {-„} (iii) C = {2n} (iv) D = (0, 00) n+3 (2) Find the supremum and infimum of the sets in question (1) above. Also find out if the supremum or infimum belong to the set or not (3) If A = {1+ "} , find out if it is bounded or not. If it is then find the upper bound , lower bound , supremum and infimu of A.
(1) Find the upper and lower bound of the following sets also state if the set is bounded or not (i) A = -{} (ii) B = {-„} (iii) C = {2n} (iv) D = (0, 00) n+3 (2) Find the supremum and infimum of the sets in question (1) above. Also find out if the supremum or infimum belong to the set or not (3) If A = {1+ "} , find out if it is bounded or not. If it is then find the upper bound , lower bound , supremum and infimu of A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![(1) Find the upper and lower bound of the following sets also state if the set is bounded or not
(i) A = -{}
(ii) B = {-}
(iii) C = {2n1}
%3D
n+3
(iv) D = (0, ∞0)
(2) Find the supremum and infimum of the sets in question (1) above. Also find out if the supremum
or infimum belong to the set or not
(3) If A = {1+ D"} , find out if it is bounded or not. If it is then find the upper bound ,
lower bound , supremum and infimu of A.
(4) Let A CR be a et ith greatet element a E A Prove that sup(A)=a
(5) Let A = {r € R+ : 2² < 2} . Explain hy A i bounded above and below and find sup(A) and inf(A).
(6)Suppose A, B CR are both non-empty subsets with a = Sup(A) and 3 = sup(B) both exist-
ing. Then if A C B then a <B.
(7) Let A = {4, 7, 8} and B = {-1,5}, Find and compare
sup(A+B) , inf(A+B), sup(A)+sup(B),sup A - inf B, inf A-inf B
(8) Prove by an example that for any set A, g.l.b(-A) = –l.u.b(A)
(9) Prove and give an example that if A and B are two bounded non-empty subset of R, then
AUB is also bounded
(10) Given that A = {-21,20, 23} and B = {1, 10, 100}, Find
(i)Sup(AU B)
(ii) inf(AU B)
(iii)min.(inf.A, Inf.B)
(iv) таz.(sup.A, sup.B)
(11) Given that A = {-12, –11, 13} and B = {-10, 20, 30}, Find
(i) g.l.b(-A)
(i) -1.и.Ь(—А)
(iii)Inf.(B – A)
(iv) Sup.(В — A)
(v) Sup.A – Sup. B)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe675df58-d6f0-423a-8749-c529271f4fa2%2Fc7051595-25e9-440a-b090-b832a203ecf5%2Fy09xadk_processed.png&w=3840&q=75)
Transcribed Image Text:(1) Find the upper and lower bound of the following sets also state if the set is bounded or not
(i) A = -{}
(ii) B = {-}
(iii) C = {2n1}
%3D
n+3
(iv) D = (0, ∞0)
(2) Find the supremum and infimum of the sets in question (1) above. Also find out if the supremum
or infimum belong to the set or not
(3) If A = {1+ D"} , find out if it is bounded or not. If it is then find the upper bound ,
lower bound , supremum and infimu of A.
(4) Let A CR be a et ith greatet element a E A Prove that sup(A)=a
(5) Let A = {r € R+ : 2² < 2} . Explain hy A i bounded above and below and find sup(A) and inf(A).
(6)Suppose A, B CR are both non-empty subsets with a = Sup(A) and 3 = sup(B) both exist-
ing. Then if A C B then a <B.
(7) Let A = {4, 7, 8} and B = {-1,5}, Find and compare
sup(A+B) , inf(A+B), sup(A)+sup(B),sup A - inf B, inf A-inf B
(8) Prove by an example that for any set A, g.l.b(-A) = –l.u.b(A)
(9) Prove and give an example that if A and B are two bounded non-empty subset of R, then
AUB is also bounded
(10) Given that A = {-21,20, 23} and B = {1, 10, 100}, Find
(i)Sup(AU B)
(ii) inf(AU B)
(iii)min.(inf.A, Inf.B)
(iv) таz.(sup.A, sup.B)
(11) Given that A = {-12, –11, 13} and B = {-10, 20, 30}, Find
(i) g.l.b(-A)
(i) -1.и.Ь(—А)
(iii)Inf.(B – A)
(iv) Sup.(В — A)
(v) Sup.A – Sup. B)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)