Exercise 4.6. Decide in each of the examples what kind of ordered set it is, poset, strict poset, linearly ordered set, or strictly linearly ordered set. (1) S = Z and R = {(r, y) | 1 < y} (2) S = Z and R = {(x, y) | x < y} (3) X a set, S = P(X) its power set, and R = {(A, B) e S × S | Ac B}. (4) X a set, S = P(X) its power set, and R = {(A, B) e S× S | Ac B}.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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This problem comes with five parts, I believe it is just identification so I hope you can solve them all! If you could also give a short explanation as to why you chose a particular identification, that would be great! 

Exercise 4.6. Decide in each of the examples what kind of ordered set it
is, poset, strict poset, linearly ordered set, or strictly linearly ordered set.
(1) S = Z and R = {(r, y) | 1 < y}
(2) S = Z and R = {(x, y) | x < y}
(3) X a set, S = P(X) its power set, and R = {(A, B) e S × S | Ac B}.
(4) X a set, S = P(X) its power set, and R = {(A, B) e S× S | Ac B}.
Transcribed Image Text:Exercise 4.6. Decide in each of the examples what kind of ordered set it is, poset, strict poset, linearly ordered set, or strictly linearly ordered set. (1) S = Z and R = {(r, y) | 1 < y} (2) S = Z and R = {(x, y) | x < y} (3) X a set, S = P(X) its power set, and R = {(A, B) e S × S | Ac B}. (4) X a set, S = P(X) its power set, and R = {(A, B) e S× S | Ac B}.
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