Find a way to partition the set of integers into 2 subsets. How do you know your subsets form a partition of the integers?

Answered: Find a way to partition the set of…

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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Find a way to partition the set of integers into 2 subsets. How do you know your subsets form a partition of the integers?

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Step 1

It is assumed that the question is asking to find a way to partition the set of all integers into two subsets. We do this as follows:

Given the set of all integers, say A. Then we first take two non-empty subsets, say B and C.

Now, for each element, say x in A, if x is an odd integer, we put it into the set B. Also, if x is the additive inverse of a positive odd integer (if x is an integer, then -x is said to be its additive inverse), then also put it in B.

Else, if the element x in A is an even integer, then put it in the set C. Same for negative integers that is if x is a negative integer and -x is an even integer, then put it in the set C.

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