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1. Consider the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10). a) Give an example of a partition S of A such that both requirements hold: • S = 3 • one of the elements of S contains only even integers b) Give an example of a partition S of A such that both requirements hold: all elements of S have the same cardinality • one of the elements of S contains only prime integers c) Give an example of a collection S of subsets of A such that S is not a partition of A.

1. Consider the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10). a) Give an example of a partition S of A such that both requirements hold: • S = 3 • one of the elements of S contains only even integers b) Give an example of a partition S of A such that both requirements hold: all elements of S have the same cardinality • one of the elements of S contains only prime integers c) Give an example of a collection S of subsets of A such that S is not a partition of A.

Advanced Engineering Mathematics
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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1. Consider the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10). a) Give an example of a partition S of A such that both requirements hold: • S = 3 • one of the elements of S contains only even integers b) Give an example of a partition S of A such that both requirements hold: all elements of S have the same cardinality • one of the elements of S contains only prime integers c) Give an example of a collection S of subsets of A such that S is not a partition of A.
Transcribed Image Text:1. Consider the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10). a) Give an example of a partition S of A such that both requirements hold: • S = 3 • one of the elements of S contains only even integers b) Give an example of a partition S of A such that both requirements hold: all elements of S have the same cardinality • one of the elements of S contains only prime integers c) Give an example of a collection S of subsets of A such that S is not a partition of A.
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