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

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Ben Brink

Posts: 201
From: Rosenberg, TX
Registered: 11/11/06
RE: Discrete Math
Posted: May 3, 2012 10:01 PM
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att1.html (2.0 K)

Great problem and a great set of proofs!

> Date: Thu, 3 May 2012 13:18:21 -0400
> From:
> To:
> Subject: Re: 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

> Yes, every integer is either even or odd but not both

> > b. the set of positive integers and the set of
> > negative integers

> No, the integer "0" is neither postive nor odd.

> > 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.

> Yes, every integer is of the form one of 3k, or 3k+1, or 3k+2 but never two of those.

> > 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.

> Yes, any integer that is not "less than -100" or "larger than 100" must be between -100 and 100 so its absolute value is less than or equal to 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.

> Yes. If a number IS divisible by 3 (so not in the first set) is a multiple of 3. If it also even, it is a multiple of 6 and so not in the third set. If it is divisible by 3 and not even, it has remainder 3 when divided by 6. (I had to reread this several times!)

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