Discrete Math Problem?

Question

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

Answer 1

I don't know the answer, but if it is a math problem, why is it in the Government section?

Answer 2

Yay, the assumption of inclusion-exclusion that distinctive human beings have not have been given a records of collectively as counting. good, A U B U C = a,b,c,d,e,g,h,ok,m,n, which has 10 aspects, so extra A n B = a,b,e, which has 3 aspects, so 3 once you do the finished intersections, in basic terms rely the quantity of aspects in each and each and replace those values into the equation. it must be a real equation after all the numbers are put in there.