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
-2.17 = 0.35r<br> what is the solution
tiny-mole [99]

Answer:

Step-by-step explanation:

r = -7.714285714

4 0
3 years ago
Read 2 more answers
To obtain the graph of y=(x- 8)2 shift the graph of y= x2
bonufazy [111]
You would shift this to the right 8 places. This is because in vertex form, the x value is the opposite of the number in the parenthesis with the x. 
6 0
3 years ago
Read 2 more answers
In which of the following numbers does the digit 9 represent 1/100 the value of the digit 9 in the number 698
kow [346]
A would be the answer to this question
3 0
3 years ago
N the figure, u ǁ v, and t is a transversal that crosses the parallel lines.
Vlada [557]
The measure of angle 4 would be the same as its opposite exterior angle which is given. It will have a measurement of 38 degrees. These angles are called alternate exterior angles. Hope this answers the question. Have a nice day. Feel free to ask more questions.
6 0
3 years ago
5 tenths plus 7 thousandths equals how many thousandths
elixir [45]
0.5 + 0.007 = 0.012
So the answer is 12 thousandths

4 0
3 years ago
Other questions:
  • Find 2p^2+3p-4 less-2p^2-3p+4
    14·2 answers
  • Is it true or false that the middle term of a perfect square trinomial is equal to 2 × √(first term) × √(last term)?
    15·1 answer
  • What is the distance between -4.5 and 3.5
    15·2 answers
  • What is the mean absolute deviation of the data set? {12, 10, 10, 8, 6, 7, 7, 12} 1 2 6 9
    5·1 answer
  • 1 What is the y-intercept of a line that has a slope of 1/4 and passes through point (8, 3)?
    6·1 answer
  • Find all real values of x that satisfy the equation x^2 - 7x = 98.
    11·1 answer
  • Can someone help me with this
    7·2 answers
  • 3) Stella drove for 300 miles to Washington D.C. and it took her six
    6·1 answer
  • Which expression is equal to 8.89? *
    12·1 answer
  • Calculate the area of triangle OPQ.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!