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Posted on 2011-09-07

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.

a. Explain why E U O belongs to Z

b. Explain why Z belongs to E U O

Thanks.

3 Comments

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.

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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