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Posted on 2011-09-07
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Let E be the set of all even integers and let O be the set of all odd integers

a. Explain why E U O belongs to Z
b. Explain why Z belongs to E U O

Thanks.
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Question by:mustish1
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Expert Comment

by:ozo
ID: 36494412
Are there any integers which are not even or odd?
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by:akajohn
akajohn earned 400 total points
ID: 36494856
This may help: The definition of parity:
http://en.wikipedia.org/wiki/Parity_(mathematics)
Integers are either odd or even. _ Just rephrasing what Ozo said.

Hence the sum of both is the list of all integers, Z.


A.
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Bardobrave earned 1600 total points
ID: 36494996
a)

Z is the collection of all integers.
E is a collection of integers
O is a collection of integers
The union of two collection of integers will be a greater collection of integers, so it has to be contained in Z

b)
All integers are even or odd (depending on if they division by 2 returns a mod of 0 or 1, so "0" is an even number).
E is the collection of all even integers (included the "0")
O is the collection of all odd integers
Z is the collection of all even and odd integers, and by definition it will be included in the union of E and O (actually it's the same).
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