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Amanda [17]
3 years ago
11

Free points *30*

Mathematics
1 answer:
Tanzania [10]3 years ago
7 0

Answer:

1 because then he would eat 6 in 6 hours .-.

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Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is:
professor190 [17]

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)\}

5 0
2 years ago
How many different arrangements are there for the word fraction?
nadezda [96]
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 = 40320.
4 0
3 years ago
Help me... :/<br><br> Find the measure of each exterior angle of a regular 45-gon.
GuDViN [60]

Answer:

7740° / 45

Step-by-step explanation:

The sum of the interior angles is given by this formula: (n - 2) * 180°. So a regular 45-gon would have interior angles that add up to: (45 - 2) * 180°. = 43 * 180°. = 7740°. Now divide that by the 45 angles to find the measure of one interior angle

hope that helped :(

7 0
3 years ago
Write as an expression :the quantity 10 less than x, divided by 4​
Andreas93 [3]

Answer:

(x-10)/4

Step-by-step explanation:

10 less than x means,

x - 10

and the divide by 4.

=> (x-10)/4

5 0
2 years ago
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HELP ASAP ILL GIVE YOU BRAINLEST
Zepler [3.9K]

Answer:

y=1 x=(∞)

Step-by-step explanation:

y-value is 1 and when the parabola is opened downward. The x-value is an infinite number choice.

4 0
3 years ago
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