prove that A relation R is called circular if aRb and bRc imply that cRa. Show that R is reflexive and circular if and only if it is an equivalence relation.

Answers

Answer 1

R is reflexive and circular if and only if it is an equivalence relation.

What is the condition for a relationship to be both reflexive and circular?

Reflexivity and circularity of R:

To prove that R is reflexive, we need to show that for every element an in the set, aRa holds. Reflexivity ensures that every element is related to itself.

To prove that R is circular, we need to demonstrate that if aRb and bRc, then cRa holds. Circular property implies that if two elements are related in one direction, they are also related in the reverse direction.

Equivalence relation:

An equivalence relation must satisfy three properties: reflexivity, symmetry, and transitivity. We have already established reflexivity in Step 1.

To show symmetry, we need to prove that if aRb, then bRa holds. However, this property is not given in the original statement of circularity.

Since R is reflexive and circular, it is an equivalence relation. However, the circular property alone is not sufficient to guarantee symmetry and transitivity, which are necessary for equivalence relations.

Therefore, R being both reflexive and circular is the condition for it to be an equivalence relation.

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Related Questions

janet buys 12 pencils for $1.49. what is the cost per pencil?

Answers

Answer:

0.124$

...............

you can simply divide the price of the pencils = 1•49$

by the number of pencils bought = 12

1•49/12

= 0•124$

Answer: 0.124166667 U.S. dollars

((1 U.S. dollar) + (49 U.S. cents)) / 12 =

0.124166667 U.S. dollars

Juan works at a health food store
two hours a day, three days a
week. His weekly pay is $73.50.
About how much does Juan make
per hour?

Give me the right answer and I’ll mark your answer the brainliest

Answers

Answer:

12.25 per hour

Step-by-step explanation:

have a great day!

The answer is 12.25.

I'm sure about the answer.

Someone please hurry, I have no idea what I am doing

Answers

Answer

61.80°

Step-by-step explanation:

use SOHCAHTOA to solve

by using SOH

sin? = 51/55

? = 1÷sin(51/55)

? = 61.80°

What integer values for a and b would make the following statement true?

Answers

Answer:

i think the values for a and b are: a=2 and b=1/4

Please help anyone will give Points

Answers

Answer:

do the base are 3 then times that twice

Step-by-step explanation:

2/8 = x/64

2/8 • 64 = x/64 • 64

128/8 = x

x = 128/8

x = 16

The volume of Figure A is 16 m³.


Hope it helps!

what does 7x^2+12x-3 equal?

Answers

Answer:

23

Step-by-step explanation:

find x=, if x-5=10 HURRY!!!!

Answers

x=15 because 15-5=10

how do i solve these using substitution

Answers

Answer:

Step-by-step explanation:

point form:

(3,4)

equation form:

x= 3,  y= 4

Cora is bringing donuts to work as a treat for her co-workers. She buys 12 donuts for $9.96. How much does each donut cost? 30 POINTS FAST NEED HELP

Answers

Divide total cost by number of donuts bought:

9.96 / 12 = 0.83

Each donut cost $0.83

Answer:

0.83

Step-by-step explanation:

number of donuts divided by price

12/9.96=1/X

X=0.83

The tickets to a high school hockey game cost either $6 or $11. A total of 540 tickets, worth $4,740, were sold. How much of the $4,740 was made from selling the $6 tickets?

Answers

Answer:

Your answer.

240

Thank you. And give my answer as Brainlist answer. Follow me for more

Step-by-step explanation:

For what value of n is 20 = {n+4?
a)
b) *
c) 40
d) 60

Answers

I think it might be 40 I’m not sure but good luck
Answer: N= 16

Explanation: 20-4=16

What is the ratio of new books to used books?
15 books 7 of these books are new . The rest of them are used

Answers

Answer:

7 to 8

Step-by-step explanation:

7-15=8

What’s the answer plz help!

Answers

Answer:

40 and 60

Step-by-step explanation:

If the radius of the glass container is 2 inches and the height is 3 inches, how much wax will she need to fill the container?

Answers

Answer:

ans is 5 container

Step-by-step explanation:

because 3+2=5

and in my first class is seen the answer

She needs to fill 12 cubic inches of wax in the container.

What is volume?

The volume of a thing is the area that it takes up in three dimensions. Simply put, objects occupy space.

Given, the radius of the glass container is 2 inches and height is 3 inches.

To fill the maximum wax in the glass container,

we will find the volume of glass container.

Volume of glass container

= Volume of cylinder.

=  π r² h

=  π(2)² (3)

=  π 4 x 3

= 12π  cubic inches.

Therefore, 12 cubic inches of wax she needs to fill.

To learn more about the volume;

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6=2(y+2) y=?

please help​

Answers

6 = 2(y + 2)
Divide by 2 on both sides.
3 = y + 2
Subtract 2 from both sides.
1 = y

(Substitution)
6 = 2(1 + 2)
6 = 2(3)
6 = 6
Answer:  y = 1

==========================================================

Explanation:

There are two ways to solve this

The first method will have us distribute the 2 through to each term, then we solve for y

6 = 2(y+2)

6 = 2y+4 .... distribute

2y+4 = 6

2y = 6-4 .... subtract 4 from both sides

2y = 2

y = 2/2 .... divide both sides by 2

y = 1 is the answer

-------------

Or we can solve through this set of steps

6 = 2(y+2)

6/2 = y+2 ...... divide both sides by 2

3 = y+2

y+2 = 3

y = 3-2 .... subtract 2 from both sides

y = 1

Either way, we get the same answer.

-------------

To check the answer, replace every copy of y with 1

Simplifying should lead to 6 on the right side

6 = 2(y+2)

6 = 2(1+2)

6 = 2(3)

6 = 6

Since we get the same thing on both sides, this means the last equation is true. This in turn means the first equation is true when y = 1. Therefore, the solution has been confirmed.

whats -5( a -6)+2a ?

Answers

Answer:

a is 4 and A is 7

Step-by-step explanation:

Answer:

89443

Step-by-step explanation:

What is the value of 3x^4?

Answers

Answer:

243

Step-by-step explanation:

[tex]5( \sqrt{ {x}^{2} + 2x - 14} + x) = 20 \\ \\ \sqrt{ {x}^{2} + 2x - 14} + x= \frac{20}{5} \\ \\ \sqrt{ {x}^{2} + 2x - 14} + x= 4 \\ \\ \sqrt{ {x}^{2} + 2x - 14} = 4 - x\\ \\ {(\sqrt{ {x}^{2} + 2x - 14} )}^{2} = {(4 - x)}^{2} \\ \\ \cancel{ {x}^{2}} + 2x - 14 = 16 - 8x + \cancel{ {x}^{2} } \\ \\ 2x - 14 = 16 - 8x \\ \\ 2x + 8x = 16 + 14 \\ \\ 10x = 30 \\ \\ x = \frac{30}{10} \\ \\ x = 3 \\ \\ 3 {x}^{4} = 3 {(3)}^{4} = 3 \times 81 \\ \\ \huge \red {3 {x}^{4}= 243}[/tex]

Another name for a cube is
A. dodecahedron
B. hexahedron
C. icosahedron
D. tetrahedron
please help

Answers

Answer:

B

Step-by-step explanation:

Find the circumference of the circle use 3.14 for that symbol help ASAP

Answers

Hello
Radius of circle =1.5cm
Therefore the circumference of the circle =2x3.14x15= 9.42cm
The answer is 9.42 cm

24 students in a class took an algebra test. if 18 students passed, what percent passed.

Answers

Answer:

75%

Step-by-step explanation:

18/24=0.75

Answer:

75%

Step-by-step explanation:

24 divided by 4 is 6, so 25% of 24 is 6. 18 divided by 6 is 3, so 18 out of 24 is 75%.

A rectangle measures 2 1/3 inches by 1 2/3 inches. What is its area?
Please simplify to a fraction and make sure its a whole and a fraction, not just the fraction!
:D

Answers

Answer:

i alr answered this correctly

Step-by-step explanation:

3 4/5

3 8/9OR3.888888888888888888888888OR35/9

HELP ASAP!!Solve for x. Enter the solutions from least to greatest.
X squared minus 5x minus 14=0
lesser x=
greater x=

Answers

x^2 - 5x - 14 = 0

what multiplies to negative 14 and adds to negative 5? -7 and positive 2.

(x - 7) (x + 2) = 0

Lesser x = -2
Greater x = 7

90% of e is 30. What is e?

Answers

Answer:

27

Step-by-step explanation:

Answer:

e = 33.3 (approx. )

Step-by-step explanation:

To find out - 'e'

Given,

90 % of e = 30

[tex] = > \frac{90}{100} \times e = 30[/tex]

[tex] = > e = 30 \times \frac{100}{90} [/tex]

[tex] = > e = \frac{100}{3} [/tex]

=> e = 33.3333......

=> e = 33.3 (approx. ) (Ans)

Karen is making 14 different kinds of greeting cards. She is making 12 of each kind. How many greeting is she making.

Answers

1?......................

PHYSICS
12 people are on the elevator to a height of 120 m. The average mass per person is 50 kg. What work does the lift engine do?​

Answers

Answer:

720000 J

Step-by-step explanation:

The formula is

Work = Force * Distance

Here we have the weight force, which is calculated as w = m * g

acceleration of gravity (g) ≈ 10 m/s

people's mass (m) = 12 * 50 kg = 600 kg

So Force = 10 m/s * 600 kg = 6000 N

Distance = 120 m

Work = Force * Distance = 6000 N * 120 m = 720000 J = 720 kJ

Help please and thank you

Answers

Step-by-step explanation:

i think it is the third choice

Find the geometric mean of 6 and 30, write your answer in simplest radical form.

Answers

Answer:

13.4

Step-by-step explanation:

The answer is 13.4!!

I need the answer ASAP!!

Answers

Answer:

it equal 23x , that the answer

Last year, Isabel opened an investment account with 6600 . At the end of the year, the amount in the account had decreased by 24.5%. How much is this decrease in dollars? How much money was in her account at the end of last year?

Answers

Answer:

a. $1,617

b. $4,983

Step-by-step explanation:

a. The account suffered a decrease of 24.5% of the original sum of $6,600.

This amount in cash is:

= 24.5% * 6,600

= $1,617

b. If the account reduced by $1,617, the balance left is:

= 6,600 - 1,617

= $4,983

A circular mirror has a diameter of 16.5 inches. What is the circumference of the mirror? Round to the nearest hundredth

Answers

Answer:

C≈51.84in

Step-by-step explanation:

C=2πr

d=2r

Solving for C

C= πd= π·16.5≈51.83628in

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