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posets are always reflexive

Nayema Laboni
Thu, 17 Dec 2015 19:49:37 GMT

, therefore, always comparable, how can a poset can be incomparable and reflexive at the same time?! Any suggestions to understand comparable and incomparable better?!

alexey
Thu, 17 Dec 2015 21:37:46 GMT

Posets themselves are not comparable or incomparable. The _elements_ in posets can be either comparable or incomparable. Do you see this? Try to come up with a poset such that there are some comparable and incomparable elements.

Nayema Laboni
Fri, 18 Dec 2015 00:13:32 GMT

but the posets are composed of elements that reflexive, transitive and antisymmetric right?! I still don't see the point here, also comparable means when you can swatch the order of a pair of elements right?!

Nayema Laboni
Fri, 18 Dec 2015 00:15:13 GMT

also connected component of graph , what properties do connected components have

alexey
Fri, 18 Dec 2015 05:21:38 GMT

The *definitions are super-important*, understand them in their entirety. Read them again, write them down, and really try spend time thinking why they are defined the way they are given in the book. Reflexivity, symmetry, anti-symmetry, and transitivity are properties of the relation R. They hold (or don't hold) *for the entire relation*. While comparable vs incomarable is the property *of any pair of elements* from the set. Any two elements are either comparable or incomarable. For example, consider the partially ordered set _(S, R)_, where _S = {0, 11, 22, 999}_, and _R={(0,0), (11,11), (22,22), (999,999), (0,11), (0,22), (11,999), (22,999)}_. *Questions:* - Is the relation _R_ a partial order relation? - For _every_ pair of elements from the set _S_, tell me if they are comparable or incomparable.

Nayema Laboni
Fri, 18 Dec 2015 05:40:19 GMT

I do the definitions, bt sometimes dey dnt wrk fr me. the ordered set will have both comparable and incomparable pairs, so in total no?!

alexey
Fri, 18 Dec 2015 06:01:04 GMT

Read the question again: "*For every pair of elements* from the set S, tell me if they are comparable or incomparable." You have to consider individually each pair, and for each pair give your answer.

alexey
Fri, 18 Dec 2015 06:41:18 GMT

Oops, there was an error in that relation _R_, it should contain the pair _(0, 999)_ too. I cannot fix that in the original reply, but it should be there.

Nayema Laboni
Fri, 18 Dec 2015 07:40:05 GMT

its alright, but before I answer that question , i think it is necessary to if I make an ordered pair (s,r), where s= (1,2), r=(3,4), my ordered pairs will be (1,3), (1,4), (2,3), (2,4) , if that's the case then , no they are not comparable

Nayema Laboni
Fri, 18 Dec 2015 19:57:29 GMT

@alexey nikolaev, when are you available in school?! I need help!

alexey
Fri, 18 Dec 2015 21:27:40 GMT

no, sorry, I'm not available in school now, and probably will not be avilable until your final. Maybe on Monday only, but try studying by yourself. And feel free asking questions here or by email.