Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Concept explainers

Set Theory
Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.
Question

Let ?0
be the set {0, 2, 12}
Let ?1
be the set {4, 5, 10}
Let ?2
be the set {6, 9, 14}
Let ?3
be the set {3, 7, 13}
Let ? be the set of non-negative integers less than 15.

Let a, be the set {0,2, 12} Let a, be the set {4,5, 10} Let az be the set {6,9, 14} Let az be the set {3,7, 13} Let A be the set of non-negative integers less than 15. (a) We need a set a, to make a partition of A. What is a4? (b) We can easily define a relation R on A that is an equivalence relation, using the 5 sets a;. Finish the sentence: For x, y E A we define R as xRy if, and only if Fill in the blank. (c) The five sets a; are the of R. Let G be the partial order relation {(a, a), (b, b), (c, c), (d, d), (e, e), (a, b), (d, e), (c, e), (b, d), (a, d), (b, e), (a, e)}. (d) Find a chain of G of size 3.
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Transcribed Image Text:Let a, be the set {0,2, 12} Let a, be the set {4,5, 10} Let az be the set {6,9, 14} Let az be the set {3,7, 13} Let A be the set of non-negative integers less than 15. (a) We need a set a, to make a partition of A. What is a4? (b) We can easily define a relation R on A that is an equivalence relation, using the 5 sets a;. Finish the sentence: For x, y E A we define R as xRy if, and only if Fill in the blank. (c) The five sets a; are the of R. Let G be the partial order relation {(a, a), (b, b), (c, c), (d, d), (e, e), (a, b), (d, e), (c, e), (b, d), (a, d), (b, e), (a, e)}. (d) Find a chain of G of size 3.
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