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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

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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 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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