1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anestetic [448]
3 years ago
10

Which of these relations on{0,1,2,3}are partial orderings? Determine the properties of a partial ordering that the others lack.

a) {(0,0),(2,2),(3,3)} b) {(0,0),(1,1),(2,0),(2,2),(2,3),(3,3)} c) {(0,0),(1,1),(1,2),(2,2),(3,1),(3,3)} d) {(0,0),(1,1),(1,2),(1,3),(2,0),(2,2),(2,3), (3,0),(3,3)} e) {(0,0),(0,1),(0,2),(0,3),(1,0),(1,1),(1,2), (1,3),(2,0),(2,2),(3,3)
Mathematics
1 answer:
omeli [17]3 years ago
3 0

Step-by-step explanation:

A = {0,1,2,3}

a): R = {(0,0),(2,2),(3,3)}

R is antisymmetric, because if the (a,b)∈R, than a=b.

R is not reflexive, because (1,1) ∉ R while 1 ∈ A.

R is transitive, because if the (a,b)∈R and (b, c) ∈ R, than a=b=c and (a,c)=(a,a)∈R.

R is not portable ordering because R is not reflexive.

b): R = {(0,0),(1,1),(2,0),(2,2),(2,3),(3,3)}

R is antisymmetric, because if the (a,b)∈R and if the (b, a) ∈ R, than a=b (since (2,0) ∈ R and (0,2) ∉ R; and (2,3) ∈ R and (3,2) ∉ R )

R is reflexive, because (a,a) ∈ R of every element a ∈ A.

R is transitive , because if the (a,b)∈R and if the ( b , c )∈R . then a = b or b = c ( since there are only two element not of the form ( a , a ) and that pair does not satisfy ( a,b ) ∈ R and ( b , a ) ∈ R ), which implies ( a , c ) = ( b , c ) ∈ R or ( a , c ) = ( a , b ) ∈ R.

R is a partial ordering, because R is reflexive, antisymmetric and transitive.

c): R =  {(0,0),(1,1),(1,2),(2,2),(3,1),(3,3)}

R is reflexive, because (a,a)∈R of every element a ∈ A.

R is antisymmetric, because if the ( a , b )∈R and if the ( b , a )∈R . then a = b ( since ( 1 , 2 )∈R and ( 2 , 1 ) ∉ R; ( 3 , 1 ) ∈ R and ( 1 , 3 ) ∉ R ).  

R is not transitive , because ( 3 , 1 ) ∈ R and ( 1 , 2 )∈R, while ( 3 , 2 ) ∈ R.

R is not a partial ordering. because R is not transitive .

d): R =  {(0,0),(1,1),(1,2),(1,3),(2,0),(2,2),(2,3), (3,0),(3,3)}

R is the reflexive, because ( a , a )∈R of every elements∈A.

R is the antisymmetric, because if the ( a , b )∈R and if the ( b , a )∈R, then a = b ( since ( 1 . 2 )∈R and ( 2 . 1 )∉R; similarly, all other elements not of the form (a,a) ).

R is not transitive, because ( 1 , 2 )∈R and ( 2 , 0 )∈R, while ( 1 . 0 )∉R.

R is not a partial ordering, because R is not transitive,

e):  R = { ( 0 , 0 ) , ( 0, 1 ) , ( 0 , 2 ) , ( 0 , 3 ) , ( 1 , 0 ) , ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 2 , 0 ) , ( 2 , 2 ) , ( 3 , 3 ) }

R is the reflexive , because ( a , a )∈R of every element a∈A .

R is not antisymmetric, because ( 1 , 0 )∈R and ( 0 , 1 )∈R while 0 is not equal to 1.

R is not transitive, because ( 2 , 0 )∈Rand ( 0 , 3 )∈R, while ( 2 , 3 )∉R .

R is not a partial ordering, because R is not the antisymmetric and not the transitive.

You might be interested in
Cuál es el menor número entero que, disminuido en 8, resulta menor que su triple
Mars2501 [29]

Answer:

-3

Step-by-step explanation:

     Let x = the number

Then 3x = its triple, and the condition is:

x - 8 < 3x

Subtract x from each side

-8 < 2x

Divide each side by 2

-4 < x

Reverse the inequality

x > -4

The smallest integer greater than -4 is -3.

Check:

-3 - 8 < 3(-3)

-11 < -9

It checks.

 

5 0
3 years ago
Solve for x with a degree of 30 &amp; side of 300ft
tankabanditka [31]

Answer:

x = 100√3


Step-by-step explanation:

tan(30º) = x/300

x = 300 tan(30º)

x = 300/√3

x = 100√3

3 0
3 years ago
Find the coordinates for the midpoint of the segment with endpoints given 12,4 and -8,8
borishaifa [10]
<h2>Hello!</h2>

The answer is:

The coordinates of the midpoint are:

x-coordinate=2\\y-coordinate=6

<h2>Why?</h2>

We can find the midpoint of the segment with the given endpoints using the following formula.

The midpoint of a segment is given by:

MidPoint=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

We are given the points:

(12,4)\\

and

(-8,8)\\

Where,

x_{1}=12\\y_{1}=4\\x_{2}=-8\\y_{2}=8

So, calculating the midpoint, we have:

MidPoint=(\frac{12+(-8)}{2},\frac{4+8}{2})

MidPoint=(\frac{4}{2},\frac{12}{2})

MidPoint=(2,6)

Hence, we have that the coordinates of the midpoint are:

x-coordinate=2\\y-coordinate=6

Have a nice day!

8 0
3 years ago
Read 2 more answers
I don't know this please help give brainlest
NARA [144]

Answer:

15x-9+y

Is required perimeter.

3 0
2 years ago
Read 2 more answers
What is the value of x enter your answer in the Box
lina2011 [118]
The x is 176.54 cm.
i use pythagorean thearem
{c}^{2}  =  {a}^{2}  +  {b}^{2}

4 0
3 years ago
Read 2 more answers
Other questions:
  • YOU WILL GET 100 PTS IF YOU ANSWER MY QUESTION CORRECTLY :D
    13·1 answer
  • There are 3 marbles (yellow,blue,and green). You pick a marble and flip a coin. How many outcomes are possible?
    6·2 answers
  • Eddie is reading a novel for English class. Has been read 173 out of 480 pages about what percent of the book has he read
    10·2 answers
  • X<br> 17- 5 +<br> 17<br> 싸<br> What is X? ?
    14·1 answer
  • The height of Maury’s room is 8.4 feet from the floor to the ceiling. Maury wants to install a ceiling fan that hangs 1.875 feet
    7·2 answers
  • Andrew plays on a basketball team. In two games he scored 2/5 of the total number of points his team scored. His team scored 55
    15·2 answers
  • Needing help with this problem​
    11·1 answer
  • Quinton answered 90% of his test questions correctly. Quinton answered 54 questions correctly.
    15·1 answer
  • Is algebra.
    13·2 answers
  • Send penis pics qaa3r3t24t​
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!