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Subject: Re: Would you post the answers to the extra problems in practice 
	test?
From: "David S." <dsnyde...@gmail.com>
To: utexas-cs313k-spring2009 <utexas-cs313k-spring2009@googlegroups.com>
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ah yes, you got me there!

On May 15, 1:12 pm, Behnam Robatmili <be...@cs.utexas.edu> wrote:
> I'm not sure if understand this example. How come y is 2 in <x.y> and =20
> then is changed to 4 in <y.z>?
>
> Behnam
>
> On May 15, 2009, at 12:38 PM, David S. wrote:
>
>
>
> > <2, 2> (R(x, y)) and <4, 4> (R(y, z)) holding gives R(x, z) as R
> > (2,4) , which is 4<4, which is false.
>
> > Therefore the relation is not transitive.
>
> > On May 15, 11:10 am, Behnam Robatmili <be...@cs.utexas.edu> wrote:
> >> I probably won't get a chance to review all the answers, but a bunch
> >> of quick comments on your answers:
>
> >> -For {<x.y>: ((natp x) =3D (natp y))}, that is right that if x and y =
=20
> >> are
> >> numbers, they are in relation, but notice that if both x and y are =20
> >> non-
> >> numbers they are also in R. For instance, (natp "ABC") =3D (natp =20
> >> '(5.6))
> >> so ("ABC".'(5.6)) is in R!
>
> >> -Why is {<x.y>: ((natp x) !=3D (natp y))} antisymmetric? Let x =3D 1 =
=20
> >> and y
> >> =3D nil for instance. R(x,y) and R(y.x) are both true but 1 !=3D nil!
>
> >> -For R =3D {<x.y>: x in N ^ y in N ^ y < 2*x}, why is it reflexive =20
> >> given
> >> that (0.0) is not in R. Also why do you think R is not transitive? =20
> >> Can
> >> you give me a counter example?
>
> >> Does that make sense?
> >> Behnam
>
> >> On May 14, 2009, at 10:51 PM, Sungjin wrote:
>
> >>> Is this right, then? I'm not really sure.
>
> >>> ;R =3D {<x.y>: ((natp x) =3D (natp y))}
> >>> ;1- Is R a relation? yes
> >>> ;2- Is R a function? no
> >>> ;3- What is dom(R)? N
> >>> ;4- What is ran(R)? N
> >>> ;5- Is R reflexive? yes
> >>> ;6- Is R irreflexive? no
> >>> ;7- Is R symmetric? yes
> >>> ;8- Is R asymmetric? no
> >>> ;9- Is R antisymmetric? no
> >>> ;10- Is R transitive? yes
> >>> ;11- Is R total? yes
> >>> ;12- Is R connected? yes
> >>> ;13- Is R an equivalence relation? yes
> >>> ;14- Is R a partial order? no
>
> >>> ;R =3D {<x.y>: ((natp x) !=3D (natp y))}
> >>> ;1- Is R a relation? yes
> >>> ;2- Is R a function? no
> >>> ;3- What is dom(R)? {v : v in N | v notin N}
> >>> ;4- What is ran(R)? Write the answer in the set notation without =20
> >>> using
> >>> R. {v: v in N | v notin N}
> >>> ;5- Is R reflexive? no
> >>> ;6- Is R irreflexive? yes
> >>> ;7- Is R symmetric? no
> >>> ;8- Is R asymmetric? yes
> >>> ;9- Is R antisymmetric? yes
> >>> ;10- Is R transitive? no
> >>> ;11- Is R total? no
> >>> ;12- Is R connected? no
> >>> ;13- Is R an equivalence relation? no
> >>> ;14- Is R a partial order? no
>
> >>> ;R =3D {<x.y>: x in N ^ y in N ^ y < 2*x}
> >>> ;1- Is R a relation? yes
> >>> ;2- Is R a function? no
> >>> ;3- What is dom(R)? {2v : v in N & v > 0}
> >>> ;4- What is ran(R)? Write the answer in the set notation without =20
> >>> using
> >>> R.
> >>> ;          {v: v in N}
> >>> ;5- Is R reflexive? yes
> >>> ;6- Is R irreflexive? no
> >>> ;7- Is R symmetric? no
> >>> ;8- Is R asymmetric? no
> >>> ;9- Is R antisymmetric? yes
> >>> ;10- Is R transitive? no
> >>> ;11- Is R total? yes
> >>> ;12- Is R connected? yes
> >>> ;13- Is R an equivalence relation? no
> >>> ;14- Is R a partial order? no
>
> >>> On 5=BF=F914=C0=CF, =BF=C0=C8=C410=BD=C308=BA=D0, David Rager <rage..=
....@gmail.com> wrote:
> >>>> You can take this as official word from the TAs that you can post
> >>>> them
> >>>> yourselves.
>
> >>>> On Thu, May 14, 2009 at 8:35 PM, Sungjin <k_o_r_e_a...@naver.com>
> >>>> wrote:
>
> >>>>> R =3D {<x.y>: ((natp x) !=3D (natp y))}
> >>>>> R =3D {<x.y>: x in N ^ y in N ^ y < 2*x}
> >>>>> R =3D {<x.y>: ((natp x) =3D (natp y))}
>
> >>>>> These three, and would you give us more examples like
> >>>>> this?- =BF=F8=BA=BB =C5=D8=BD=BA=C6=AE =BC=FB=B1=E2=B1=E2 -
>