6. (a) Let A, B, be subsets of R. State the conditions which make the pair (A, B) Dedekind cut. (b) Let A, B, D, E and F be subsets of R defined as follows: A = {r €R: 1<5}, B= {r €R: r> 5}, D= {r €R: r< 5}, E = {r € R: r26} and F = {r €R: r 2 5}. State with reason(s) whether or not each of the following is a Dedekind cut. i. (А, В). i. (А, F). iii. (D, F). iv. (A, E).

6. (a) Let A, B, be subsets of R. State the conditions which make the pair (A, B) Dedekind cut. (b) Let A, B, D, E and F be subsets of R defined as follows: A = {r €R: 1<5}, B= {r €R: r> 5}, D= {r €R: r< 5}, E = {r € R: r26} and F = {r €R: r 2 5}. State with reason(s) whether or not each of the following is a Dedekind cut. i. (А, В). i. (А, F). iii. (D, F). iv. (A, E).

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

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6. (a) Let A, B , be subsets of R. State the conditions which make the pair (A, B)
Dedekind cut.
(b) Let A, B, D, E and F be subsets of R defined as follows:
A = {r €R: 1<5}, B= {r €R: r> 5}, D= {r € R: r < 5} ,
E = {r € R : r> 6} and F = {r € R: r > 5}.
State with reason(s) whether or not each of the following is a Dedekind cut.
i. (А, В).
ii. (A, F).
iii. (D, F).
iv. (A, E).

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