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Questions and exercises

1. Indicate which of the following statements are correct and which are not.

a.<<1,2>,<1,3>>is an ordered pair.

b. Any set of ordered pair is a binary relation.

c. {<1,2>,<1,3>,<2,3>} is less than relation on {1,2,3}

d. {1,2} × {3} = {<1,3>,<2,3>,<3,1>,<3,2>}

2. Indicate which of the following statements are correct and which are not.

a. Any set of quadruplets is a 4-ary relation.

b. {<1,2,1>} is a ternary relation on the set of natural numbers.

c. {1,2} × {3} × {4,5} = {1,2} × {4,5} × {3}

d. {<1,2,{1,2}>,<2,3,{2,3}>,<3,1,{1,3}>} is a ternary relation.

3. Indicate which of the following statements are correct and which are not.

a. {<1,2>,<2,3>} is equal to {<1,2>,<2,3>} as a relation.

b. The relation {<1,1>,<2,2>} over {1,2} is equal to the relation {<1,1,1>,<2,2,2>} over {1,2}.

c. The relation {<1,2>,<2,1>} over {1,2} is equal to the relation {<1,2>,<2,1>} over {1,2,3}.

d. The relation {<1,2>,<2,1>} over {1,2} is equal to the relation {<1,2>,<2,1>,<1,2>} over {1,2}.

4. For the graph in Figure 11, indicate which of the following statements are correct and which are not.

a. The in-degree of vertex 2 is 3.

b. Every partial digraph with vertices 2,4 and 5 is connected.

c. 22 is a loop.

d. 213 is a simple directed path.

5. Indicate which of the following statements are correct and which are not.

a. A binary relation on a set can be neither symmetric nor anti-symmetric.

b. For a transitive relation, only vertices connected by a directed path are connected by an arc.

c. If a relation R is symmetric, then for every<a,b>in R<b,a>must be in R.

d. A symmetric relation cannot be transitive an irreflexive at the same time.

6. Indicate which of the following statements are correct and which are not.

a. The intersection of less-than-or-equal-to and greater-than-or-equal-to relations is quality relation.

b. If B is a binary relation on a set A and T is a ternary relation on A, union of B and T is a relation.

c. If<a,b>is in RR, then b can reached from a in 2 or less hops in the digraph of R.

d. The square of less-than-or-equal-to relation is equal to less-than-or-equal-to relation.

7. Indicate which of the following statements are correct and which are not.

a. The symmetric closure of a relation is a relation, and it is symmetric.

b. The transitive closure of a relation contains all the ordered pairs of the relation, and possibly more.

c. If a relation is symmetric, then it is its own symmetric closure.

d. If the digraph of a relation is a simple cycle, then its transitive closure is the universal relation.

8. Indicate which of the following statements are correct and which are not.

a. An equivalence relation must be symmetric.

b. An equivalence relation can be antisymmetric.

c. Objects in different equivalence classes may be related to each other.

d. An equivalence relation is the universal relation on each of its equivalence classes.

9. Indicate which of the following statements are correct and which are not.

a. A total order is a partial order.

b. The partial order can be reconstructed from a Hasse diagram.

Questions & Answers

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Discrete structures. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10768/1.1
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