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Topic: Discrete Math
Replies: 8   Last Post: May 18, 2012 4:00 AM

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Ben Brink

Posts: 198
From: Rosenberg, TX
Registered: 11/11/06
RE: Discrete Math
Posted: Apr 11, 2012 8:03 PM
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Wishwy,
For a "partition", don't we need sets that are pairwise disjoint (no pair has any elements in common) where the union of all the sets is the set of integers? For example, in (b) if we "union" the positive and even integers, is that ALL the integers?
Thanks for an interesting problem!
Ben


> Date: Wed, 11 Apr 2012 19:53:20 -0400
> From: discussions@mathforum.org
> To: discretemath@mathforum.org
> Subject: Discrete Math
>
> Which of these collections of subsets are partitions of the set of integers?
>
> a. the set of even and the set of odd numbers
> b. the set of positive integers and the set of negative integers
> c. the set of integers divisible by 3, the set of integers leaving a remainder 1 when divided by 3, and the set of integers leaving a remainder of 2 when divided by 3.
> d. the set of integers less than -100, the set of integers with absolute value not exceeding 100, and the set of integers greater than 100.
> e. the set of integers not divisible by 3, the set of even integers, and the set of integers that leave a remainder of 3 when divided by 6.





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