11. Show that (a) A - B = An BC (b) An (B UC) = (ANB) U (ANC), AU (BNC) = (AUB) n (AUC) (c) (AUB) = Aºn Bº, (An B) = AC U BC (d) {x € Rx > 0} = U%-₁{x € R|x > 1/n} 12. (a) Show that the function defined by f(x) from its domain to its range, Find the inverse f-¹. -1 (b) Define a function F:F: R XR → RX R as follows: For all (x, y) e R XR, F(x, y) = (x + y, x - y). Show that F is one to one and onto, and find its inverse F-1. 2 x+1 2x-3' = (x + 2) is one to one and onto
11. Show that (a) A - B = An BC (b) An (B UC) = (ANB) U (ANC), AU (BNC) = (AUB) n (AUC) (c) (AUB) = Aºn Bº, (An B) = AC U BC (d) {x € Rx > 0} = U%-₁{x € R|x > 1/n} 12. (a) Show that the function defined by f(x) from its domain to its range, Find the inverse f-¹. -1 (b) Define a function F:F: R XR → RX R as follows: For all (x, y) e R XR, F(x, y) = (x + y, x - y). Show that F is one to one and onto, and find its inverse F-1. 2 x+1 2x-3' = (x + 2) is one to one and onto
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
solve these three problems (#11,#12,#13)
![11. Show that
(a) A B = An BC
(b) An (BUC) = (A n B) u (ANC), AU (BNC) = (A U B) n (AUC)
(c) (AUB) = Aº ʼn Bº, (A n B)¢ = Aº U Bº
(d) {x = R]x > 0} = U%-1{x € R[x > 1/n}
x+1
2x-3'
12. (a) Show that the function defined by f(x)
from its domain to its range, Find the inverse f¹.
(b) Define a function F:F: R × R → R × R as follows: For all (x, y) € R XR,
F(x, y) = (x + y,x - y).
Show that F is one to one and onto, and find its inverse F-1.
2
(x = ) is one to one and onto
13. Suppose that the function f: X → Y is a one to one and onto, with inverse f¹: Y →
X. Show that f¹ ofƒ =Ỉx, and ƒ • ƒ˜¹ = Ỉy.
O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9656a833-2928-468d-bda4-7d65920b0a10%2Fe1617786-9771-433a-963d-162387ec70b8%2Fbprqbel_processed.png&w=3840&q=75)
Transcribed Image Text:11. Show that
(a) A B = An BC
(b) An (BUC) = (A n B) u (ANC), AU (BNC) = (A U B) n (AUC)
(c) (AUB) = Aº ʼn Bº, (A n B)¢ = Aº U Bº
(d) {x = R]x > 0} = U%-1{x € R[x > 1/n}
x+1
2x-3'
12. (a) Show that the function defined by f(x)
from its domain to its range, Find the inverse f¹.
(b) Define a function F:F: R × R → R × R as follows: For all (x, y) € R XR,
F(x, y) = (x + y,x - y).
Show that F is one to one and onto, and find its inverse F-1.
2
(x = ) is one to one and onto
13. Suppose that the function f: X → Y is a one to one and onto, with inverse f¹: Y →
X. Show that f¹ ofƒ =Ỉx, and ƒ • ƒ˜¹ = Ỉy.
O
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
