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ThisGuy
Posts:
2
From:
everywhere
Registered:
5/3/12


Re: Discrete Math
Posted:
May 3, 2012 1:18 PM


> 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!)



