Hello,
I can't figure out the problem below. Any help would be greatly appreciated. Thank you!
Let R be a relation on the set N of natural numbers defined by
R = {(a,b) (element symbol) N x N ׀ a divides b in N }
Is R a partial order of N? Explain.
Is N with the divisibility relation given above a totally ordered set? Explain.
Here is my work so far:
Reflexive: so, a <= a always holds.
For example, 2 <= 2
3 <= 3
...etc.
Antisymmetric: so, if a <= b and b <= a holds, then a = b
Don't see this yet? What values to choose to show? Can a and b be the same value?
Transitive: so, if a <= b and b <= c hold, then a <= c also holds.
For Example, since 2 <= 3, and
3 <= 6, then
2 <= 6
* I need to know the antisymmetric part before I can tell if it holds and therefore is a poset.
To be totally ordered every pair of elements a,b in the set is comparable (a <=b or b <= a). The set of natural numbers is not totally ordered since for example
2007-02-27
07:25:59
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2 answers
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asked by
MathStudent3
1