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
Zolol [24]
3 years ago
13

Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is:

Mathematics
1 answer:
professor190 [17]3 years ago
5 0

Answer:

Remember, if B is a set, R is a relation in B and a is related with b (aRb or (a,b))

1. R is reflexive if for each element a∈B, aRa.

2. R is symmetric if satisfies that if aRb then bRa.

3. R is transitive if satisfies that if aRb and bRc then aRc.

Then, our set B is \{1,2,3,4\}.

a) We need to find a relation R reflexive and transitive that contain the relation R1=\{(1, 2), (1, 4), (3, 3), (4, 1)\}

Then, we need:

1. That 1R1, 2R2, 3R3, 4R4 to the relation be reflexive and,

2. Observe that

  • 1R4 and 4R1, then 1 must be related with itself.
  • 4R1 and 1R4, then 4 must be related with itself.
  • 4R1 and 1R2, then 4 must be related with 2.

Therefore \{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(4,1),(4,2)\} is the smallest relation containing the relation R1.

b) We need a new relation symmetric and transitive, then

  • since 1R2, then 2 must be related with 1.
  • since 1R4, 4 must be related with 1.

and the analysis for be transitive is the same that we did in a).

Observe that

  • 1R2 and 2R1, then 1 must be related with itself.
  • 4R1 and 1R4, then 4 must be related with itself.
  • 2R1 and 1R4, then 2 must be related with 4.
  • 4R1 and 1R2, then 4 must be related with 2.
  • 2R4 and 4R2, then 2 must be related with itself

Therefore, the smallest relation containing R1 that is symmetric and transitive is

\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}

c) We need a new relation reflexive, symmetric and transitive containing R1.

For be reflexive

  • 1 must be related with 1,
  • 2 must be related with 2,
  • 3 must be related with 3,
  • 4 must be related with 4

For be symmetric

  • since 1R2, 2 must be related with 1,
  • since 1R4, 4 must be related with 1.

For be transitive

  • Since 4R1 and 1R2, 4 must be related with 2,
  • since 2R1 and 1R4, 2 must be related with 4.

Then, the smallest relation reflexive, symmetric and transitive containing R1 is

\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}

You might be interested in
If bc is the diameter of the circle below, what is the area of the circle
dangina [55]

Answer:

option a.

radius of the circle=3 units.

area of the circle= pi×r²

area of circle=pi×3²

area of circle=pi×9units²

5 0
3 years ago
Read 2 more answers
If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),
Marrrta [24]

Answer:

a = 3

b = 2

c = 0

d = -4

Step-by-step explanation:

Form 4 equations and solve simultaneously

28 = a(2)³ + b(2)² + c(2) + d

28 = 8a + 4b + 2c + d (1)

-5 = -a + b - c + d (2)

220 = 64a + 16b + 4c + d (3)

-20 = -8a + 4b - 2c + d (4)

(1) + (4)

28 = 8a + 4b + 2c + d

-20 = -8a + 4b - 2c + d

8 = 8b + 2d

d = 4 - 4b

Equation (2)

c = -a + b + d + 5

c = -a + b + 4 - 4b+ 5

c = -a - 3b + 9

28 = 8a + 4b + 2c + d (1)

28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b

28 = 6a - 6b + 22

6a - 6b = 6

a - b = 1

a = b + 1

220 = 64a + 16b + 4c + d (3)

220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b

220 = 60b + 100

60b = 120

b = 2

a = 2 + 1

a = 3

c = -3 - 3(2) + 9

c = 0

d = 4 - 4(2)

d = -4

8 0
3 years ago
Read 2 more answers
The estimated regression equation is = 7.6 + .9x. what is the value of the standard error of the estimate (to 2 decimals)?
kupik [55]
Any answer things? :/
4 0
3 years ago
A portion of the Quadratic Formula proof is shown. Fill in the missing reason
Dahasolnce [82]

Answer:

The first one

Step-by-step explanation:

I believe it is the first option, as you can see that, on the right hand side, 4a was multiplied to the first term to make a common denominator. I'm sorry if it is wrong, and I hope this helped.

5 0
3 years ago
Read 2 more answers
How do you find the measure of each
bogdanovich [222]
Um, so it's a bit awkward with this question because they actually got the x value incorrect. When they added up all the values, they got 9x - 27 = 180, but it's actually 9x + 27 = 180 because -18 + 45 is positive 27. Anyways, when you solve it correctly you get x = 17, and then you substitute it into the angles. So with 5x - 18, you are saying 5(× 17) - 18 = 67. Then with the other one you do 4(× 17) + 45 = 113. You know that x is definitely 17 because 113 + 67 = 180.
4 0
3 years ago
Other questions:
  • Can y’all answer the question for me please
    7·1 answer
  • The equation of motion for a particle in meters at time t seconds is s(t)=sin(pi(t)/6)+cos(pi(t)/6), 0 is less then/equal to t i
    8·1 answer
  • you are purchasing four items and you want to calculate the tax. The items cost 2.50, 8.75, 3.00, and 10.25. The tax rate is 6%.
    12·1 answer
  • -3x-7(x+4) which is a term in this expression
    15·1 answer
  • AB is the perpendicular bisector of XY. Point P is the midpoint of XY. Which of the following are true?
    12·1 answer
  • Is my proportion right or wrong...if not what is the correct answer?!!
    15·2 answers
  • Help me please answer this, this will be my first grade for freshman year. The picture of the question is down below.
    15·1 answer
  • Find the midpoint of the segment with the following endpoints. (-10,2) and (-5,-1)
    10·2 answers
  • HELP I NEED THESE FOR TODAY MOST BRAINIEST FOR THE FIRST :)!!
    15·1 answer
  • Can anyone help me find the area of these two pls ? ty
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!