Decide whether the set S = {−1, 0 ,1} is closed under each of the following operations. Be sure to justify
each of your conclusions.

1. Multiplication
2. Addition
3. Subtraction
4. Division
5. Squaring
6. Square rooting
7. Averaging 2 numbers
8. Averaging 3 numbers

Answers

Answer 1

Answer:

Explained below

Step-by-step explanation:

Sol: 1. Multiplication

Multiply the set S; the answer should also belong to the set S. For example, -1 x 0 = 0 Є S and -1 x 1 = -1 Є S, Hence the set S is closed under multiplication.

2. Addition

When we add two sets S elements, the answer should also belong to the set S, for example, 1 + 0 = 1 Є S but 1 + 1 = 2, which does not belong to set S; hence S is not closed under addition.

3. Subtraction

The set S is not closed under subtraction because  -1 – 1  = -2, -2 is not the set S.

4. Division

The set S is not a closed division because when we divide one S element to another element, the answer does not belong to the set S, for example -1/0 = undefined.

5. Squaring

The set is closed under squaring if we square an element of the set S, and the result also belongs to the set S, for example, (0)2 = 0 and (-1)2 = 1, which belongs to the set S. Hence set S is closed under squaring.

6. Square rooting

The set S is not closed under square rooting because when we take the square root of an element of set S, the answer does not belong to the set S. √-1 = undefined.

7. Averaging two numbers

Averaging two numbers mean the sum of two numbers of set S is divided by two. For example, 1 + 0/2 = 1/2, which is not belongs to set S. hence set is not closed under averaging two numbers.

8. Averaging three numbers

The sum of three numbers of set S is divided by 3; the answer should belong to the set S.

-1 + 0 + 1 / 3= 0, 0 belongs to set. Hence the set S is closed under averaging three numbers.

Answer 2

Answer is explained below. We can say that Subtraction is not closed under the set.

Given set S = {−1, 0 ,1}  we have to check the given set is closed or not.

1. Multiplication

Multiply the set S; the answer should also belong to the set S. For example, [tex]-1\times 0=0[/tex], 0 Є S and [tex]-1\times 1 = -1[/tex] , -1 Є S, so the set S is closed under multiplication.

2. Addition

On adding the any two values of the set, the result belong to the set itself, for ex if we add [tex]-1+0=-1\\[/tex] Є S  but 1. so we can say that the given set is closed under addition.

3. Subtraction

The set S is not closed under subtraction because  -1 – 1  = -2, -2 is not the set element S.

4. Division

The set S is not belongs to closed division because when we divide one S element to another element, the answer does not belong to the set S, for example -1/0 = undefined.

5. Squaring

The set is closed under squaring,since we square an element of the set S, and the result also belongs to the set S. for example, [tex]0^{2} =0[/tex] and[tex]-1^{2} =1[/tex] which belongs to the set S. Hence set S is closed.

Hence We can say that Subtraction is not closed under the set.

For more details on Set follow the link below:

https://brainly.com/question/8053622


Related Questions

A pattern of increasing perfect squares is shown below.

25, 36, 49, 64, _, 100

What number do you need to find the square to find the missing term?

A. 6
B. 8
C. 7
D. 9

Answers

the answer is d. 9 hope this helps
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3x + 5 =11 use the subtraction property of equality

Answers

2 subtract 5 from both sides, cancel out 5 in left. 3x=6 divide 3 from both sides so x=2

Answer: the answer to the equation would be x=2

Step-by-step explanation:

You would use the subtraction property of equality to get ride of the five. Then you would subtract 11 by 5 and get 6. After that you would get the x by itself and divide it by 3. Them you will also divide 6 by 3 And be left with 2.

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Answers

Answer:

3×2 + 3×-b

Step-by-step explanation:

[tex]3(2-b)\\= 3\times 2 + 3\times (-b)\\\\= 6 -3b[/tex]

3(2-b) can be rewritten as 3•2 - 3b

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Answers

Answer: 26/3

Step-by-step explanation: When dividing by a fraction, we can change

the division sign to multiplication and flip the second fraction.

So 13/2 ÷ 3/4 means the same thing as 13/2 · 4/3.

So when dividing by a fraction, we can just multiply

by the reciprocal of that fraction or that fraction flipped.

Next we cross-cancel.

4 and 2 reduce to 2 and 1.

Multiplying across the numerator and denominators we have 26/3.

Smita is experimenting with how a paper airplane's shape affects the distance it will fly. Which action is the result of her logical reasoning? A. She follows her procedure carefully. B. She decides to use the same type of paper for each airplane. C. She decides to perform the experiment outside on a windy day. D. She records only the data that support her favorite hypothesis.​

Answers

Answer:

She decides to use the same type of paper for each airplane

Step-by-step explanation:

Answer:

b just did it

Step-by-step explanation:

Solve 3[-x + (2 x + 1)] = X-1.
X =

Answers

X= -2

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Answer:

-2

Step-by-step explanation:

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Using the table given below, find the number of Tourist Resorts per capita in Istanbul. Write your answer as a decimal correctly rounded to 6 places Write your answer above in scientific notation. Example: 2.9x10^-1 OR 5.8E6 City Population Tourist Resorts Beijing 20.035 million 290 Mexico City 21.671 million 348 Istanbul 15.154 million 160 Paris 11.017 million 232

Answers

Answer:

0.0000111.1E-5

Step-by-step explanation:

In Istanbul, the number of resorts per person is ...

  160/(15.154·10^6) = 0.000011 . . . . rounded to 6 places

  = 1.1E-5 . . . . in scientific notation

Which type of transformation is shown here?

Answers

That would be a rotation

Answer:

this one is Rotation

Step-by-step explanation:

it's going to flip on the side

what is the answer for -9+x=-26

Answers

x=-17 is the answer

Answer:

x =-17

Step-by-step explanation:

[tex]-9+x=-26\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\-9+x+9=-26+9\\\\Simplify\\x=-17[/tex]

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Answers

Answer:

Class width = 9

Class limits = 20 - 28; 20 - 28; 29 - 37; 38 - 46; 47 - 55; 56 - 64; 65 - 73; 74 - 82.

Step-by-step explanation:

We are given;

Highest value = 82

Lowest value = 20

Frequency = 7

Formula for class width is;

Class width = (Highest Value - Lowest Value)/number of classes

Class width = (82 - 20)/7

Class width = 8.8 ≈ 9

Now,since class width is 9, limits between 20 and 82 would be done at intervals of 9.

Thus;

Class limits = 20 - 28; 20 - 28; 29 - 37; 38 - 46; 47 - 55; 56 - 64; 65 - 73; 74 - 82.

I will give the brainiest

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What is the price of one movie ticket without the coupon?
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$11
$9
$7

Answers

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

1/2 multiplied by 4/3= 2/3

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Answers

Answer:

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Step-by-step explanation:

[tex]rate~of~change = \dfrac{f(x_2) - f(x1)}{x_2 - x_1}[/tex]

[tex]rate~of~change = \dfrac{f(x_2) - f(x1)}{x_2 - x_1}[/tex]

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[tex] f(x_1) = f(0) = \dfrac{-7(0)^3}{(0)^4 - 1} [/tex]

[tex] f(x_1) = \dfrac{0}{-1} = 0 [/tex]

[tex] f(x_2) = f(0.3) = \dfrac{-7(0.3)^3}{(0.3)^4 - 1} [/tex]

[tex]f(x_2) = \dfrac{-0.189}{-0.9919} = 0.190543[/tex]

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Answers

Answer:

m=

[tex] \frac{4}{5} [/tex]

Step-by-step explanation:

Slope of a line is the co efficient of x in the given line.

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Answers

Answer:

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Step-by-step explanation:

What are factors in the expression 4x(3x^2+5y)

Answers

Answer:

12x^3 +20xy

Step-by-step explanation:

Hope this Helped!!!!!!!!!!!!

Answer:

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Step-by-step explanation:

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I NEED HELP!!!!!! 4x+2x-5=7x-1

Answers

Let's solve your equation step-by-step.

4x+2x−5=7x−1

Step 1: Simplify both sides of the equation.

4x+2x−5=7x−1

4x+2x+−5=7x+−1

(4x+2x)+(−5)=7x−1(Combine Like Terms)

6x+−5=7x−1

6x−5=7x−1

Step 2: Subtract 7x from both sides.

6x−5−7x=7x−1−7x

−x−5=−1

Step 3: Add 5 to both sides.

−x−5+5=−1+5

−x=4

Step 4: Divide both sides by -1.

−x

−1

=

4

−1

x=−4

Answer:

x=−4

i hope this helps you

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Answers

Margaret: -9
Anika: +1
Johan: 0
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Step-by-step explanation:

Minus(minus) gives plus(+)

The diagonals of a rhombus are 4 inches and 18 inches. How long are the sides?

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Answers

Step-by-step explanation:

7n-5n=6

2n=6

n=6/2

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c, LMJ and IJM

they are corresponding angles :)

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Answers

Answer:

4

Step-by-step explanation:

[tex]\sqrt{15}\\=3.87298\dots \\\\= 4[/tex]

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Answers

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Answers

That show work from me

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Answers

Answer:

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Answers

Answer:

x = 1 , y = 1 , z = -3

Step-by-step explanation:

Solve the following system:

{3 x + 2 y - z = 8

2 x + 2 z = -4

x + 3 y = 4

Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for x:

{3 x + 2 y - z = 8

2 x + 2 z = -4

x + 3 y = 4

Hint: | Solve for x.

Subtract 3 y from both sides:

{3 x + 2 y - z = 8

2 x + 2 z = -4

x = 4 - 3 y

Hint: | Perform a substitution.

Substitute x = 4 - 3 y into the first and second equations:

{3 (4 - 3 y) + 2 y - z = 8

2 (4 - 3 y) + 2 z = -4

x = 4 - 3 y

Hint: | Expand the left hand side of the equation 3 (4 - 3 y) + 2 y - z = 8.

3 (4 - 3 y) + 2 y - z = (12 - 9 y) + 2 y - z = 12 - 7 y - z:

{12 - 7 y - z = 8

2 (4 - 3 y) + 2 z = -4

x = 4 - 3 y

Hint: | Expand the left hand side of the equation 2 (4 - 3 y) + 2 z = -4.

2 (4 - 3 y) + 2 z = (8 - 6 y) + 2 z = 8 - 6 y + 2 z:

{12 - 7 y - z = 8

8 - 6 y + 2 z = -4

x = 4 - 3 y

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for y:

{12 - 7 y - z = 8

8 - 6 y + 2 z = -4

x = 4 - 3 y

Hint: | Isolate terms with y to the left hand side.

Subtract 12 - z from both sides:

{-7 y = z - 4

8 - 6 y + 2 z = -4

x = 4 - 3 y

Hint: | Solve for y.

Divide both sides by -7:

{y = 4/7 - z/7

8 - 6 y + 2 z = -4

x = 4 - 3 y

Hint: | Perform a substitution.

Substitute y = 4/7 - z/7 into the second equation:

{y = 4/7 - z/7

8 - 6 (4/7 - z/7) + 2 z = -4

x = 4 - 3 y

Hint: | Expand the left hand side of the equation 8 - 6 (4/7 - z/7) + 2 z = -4.

8 - 6 (4/7 - z/7) + 2 z = 2 z + ((6 z)/7 - 24/7) + 8 = (20 z)/7 + 32/7:

{y = 4/7 - z/7

(20 z)/7 + 32/7 = -4

x = 4 - 3 y

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for z:

{y = 4/7 - z/7

(20 z)/7 + 32/7 = -4

x = 4 - 3 y

Hint: | Isolate terms with z to the left hand side.

Subtract 32/7 from both sides:

{y = 4/7 - z/7

(20 z)/7 = -60/7

x = 4 - 3 y

Hint: | Solve for z.

Multiply both sides by 7/20:

{y = 4/7 - z/7

z = -3

x = 4 - 3 y

Hint: | Perform a back substitution.

Substitute z = -3 into the first equation:

{y = 1

z = -3

x = 4 - 3 y

Hint: | Perform a back substitution.

Substitute y = 1 into the third equation:

{y = 1

z = -3

x = 1

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = 1 , y = 1 , z = -3

Complete the paragraph proof. We are given that Ray E B bisects ∠AEC. From the diagram, ∠CED is a right angle, which measures degrees. Since the measure of a straight angle is 180°, the measure of angle must also be 90° by the . A bisector cuts the angle measure in half. m∠AEB is 45°.

Answers

Answer:

1. 90

2. AEC

3. angle addition postulate

:)

Answer:

answers

Step-by-step explanation:

What is is the answer of 2/4+3/8=

Answers

Answer:

7/8

Step-by-step explanation:

2/4+3/8= 4/8+3/8=7/8

7/8 is your answer .............
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