Use an element argument to prove the statement. (Assume that all sets are subsets of a universal set U.)

Statement: For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) − B.

Answers

Answer 1

Answer and Step-by-step explanation:

Solution:

Given:

A, B and C are sets.

We have to prove that:

(A − B) ∩ (C − B) = (A ∩ C) − B.

Use an element x,

Let x Є (A – B), by the definition of difference:

X Є A  and x ∉ B.

And

X Є A ∩ C and x ∉ B

X Є (A ∩ C) – B

Now let x Є C – B

By the definition of difference:

X Є C and x ∉ B

By definition of intersection: x Є C and x Є( A ∩ C)  

By definition of difference, using that x Є(A ∩ C) And x  ∉ B:

X Є ( A ∩ C) – B

We know that: x Є (A – B) ∩ ( C – B)

Is equivalent to x Є A – B  and x Є C – B

So, ( x Є A and x ∉ B)

And (x Є C and x  ∉  B)

From this we know that x Є (A ∩ C) – B.


Related Questions

The singularity of a galactic dying star creates a 4th dimensional outbreak. how would you deter the event horizon. if the expansion of the black hole is 1.0034ct per second.

current mass- 2.078 wid
mass of singularity- 00.01 wid

zero light emission, even horizon as of zero known to occur

Answers

If u tam 2.078 and divide it by .01 u get 2.078 so ur answer is 2.078

The mean score on a calculus exam was 40 and the standardize deviation was five. The teacher decided to double everyone score and then add seven points. What are the values of the mean and standard deviation of the distribution of transform exam scores

Answers

Answer:

The mean will double and add 7, the SD will double

Step-by-step explanation:

If the old mean is x, the new mean will be 2x+7, and since the SD is based on x, the SD for after the curve will based on 2x, so it will also double.

PLEASE HELP ME OUT HEREEEEEEEE

Answers

Answer:

7/10

Step-by-step explanation:

4 1/5 - 3 1/2 = 7/10

Help!! Stefan sells Jin a bicycle for $105 and a helmet for $16. The total cost for Jin is 110% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin? Stefan originally spent $​

Answers

Answer:

110

Step-by-step explanation:

I got it right and I know it's been two weeks but this is just to help anyone else who sees this

Which of these is a linear equation in
standard form for the graph shown?

Answers

Answer:

B

Step-by-step explanation:

Because the slope is a positive slope (goes through the positive quandrants on the graph), we can eliminate answer choices c. Now, if we solve a, b, and d and we can see if the slope + y-intercept matches the graph.

For A.) (solve for y to get a y=mx + b equation)

3x-2y=4

-2y= -3x + 4

y= 3/2 -2

For B.)

3x-2y= -4

-2y= -4-3x

y= 3/2 + 2

For D.)

2x+3y= 4

3y= 4-2x

y= -2/3x + 4/3

Now, if we look at D, the slope is negative so it cannot be D. That leaves us with A and B. The b in the y=mx + b equation stands for the y-intercept, so we can see that the y-intercept is 2. So, since the graph intersects the y-axis at (0,2), the answer is B! y=3/2 + 2 has a positive slope and 2 for the y-intercept!

What is 10m + 12n - 5m + 3n + 5

Answers

Answer:

35 if the n are m but while im her pla help me with my question i rilly need the answer its ergent thnx

Step-by-step explanation:

Answer:

5m+15n+5

Step-by-step explanation:

Combine like terms

10m-5m = 5m

12n+3n = 15n

5m+15n+5

6 Adult tickets + 5 kids tickets = 112.50$ Day 1


Day 2

8 adult tickets + 4 kid tickets = 130$
Please explain

How much do the tickets cost for A adult tickets or

C kids tickets for both days?

Answers

Answer:

Adult : $12.5 per ticket

Kids: $7.5 per ticket

Day 1

Adult tickets were $75

Kids tickets were $37.5

Day 2

Adult tickets were $100

Kids tickets were  $30

Step-by-step explanation:

Answer:

The first Day for Adults it cost 18.75 and for the kids it cost 22.5

The Second Day for the Adults is 16.25 and for the kids it is 32.5

Step-by-step explanation:

The way I Solved this is i took the amount it cost a didved it by how many Adult tickets there were and how many Kids tickets there and there you go. Super Easy!!

Represent the following sentence as an algebraic expression, where "a number" is the letter x. 8 is added to a number​

Answers

Answer:

x+8

Step-by-step explanation:

"a number" is x? And it is added to 8.

Graph
y - 6 = 4 ( x - 4 )

Answers

Step-by-step explanation:

First, we need to get it to slope-intercept form:

So you distribute the 4 to x-4:

4x-16

now the equation looks like this:

y-6=4x-16

now move the -6 to the other side:

y=4x-10

Answer:

The graph of the equation y - 6 = 4(x - 4) is attached at the end.

To graph the equation y - 6 = 4(x - 4), rewrite it in slope-intercept form by solving for y:

y - 6 = 4(x - 4)

y - 6 = 4x - 16

y = 4x - 16 + 6

y = 4x - 10

Now, the slope (m) is 4 and the y-intercept (b) is -10.

To graph the equation, plot a few points and draw a straight line passing through those points.

Choose some x-values and calculate the corresponding y-values:

For x = 0, y = 4(0) - 10 = -10

For x = 2, y = 4(2) - 10 = -2

For x = 4, y = 4(4) - 10 = 6

For x = 6, y = 4(6) - 10 = 14

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What's greater -5/7 or -2/7

Answers

Answer:

-2/7

Step-by-step explanation:

thats how math works?

The estimated population is 1242 and the actual population is 1378.

The percent error is approximately

Answers

15- bco i know hope this helps

The percentage error is approximately 10%

How to estimate the percent error?

We have:

Estimated = 1242

Actual = 1378

The change in the measurement is:

Change = Actual - Estimate

So, we have:

Change = 1378 - 1242

Evaluate

Change = 136

The percentage error is then calculated as:

Percentage error = Change * 100%/Actual

This gives

Percentage error = 136 * 100%/1378

Evaluate

Percentage error = 9.869%

Approximate

Percentage error = 10%

Hence, the percentage error is approximately 10%

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please give me the answer for 8,9,10,11,12 and 13 please will give 25 points.

Answers

Answer:

8 ,d=4       9, -3e/2=-24  10, all real numbers  11, p=9/2 12, x=10 13, No Solution

Step-by-step explanation:

If any of these are incorrect I apologize but you are in college and you did not mention if you took calculus trigonometry or Statistics if they are wrong tell me what class it is you take and I will gladly fix them for you :D

At the Kennel, the ratio of dogs to cats is 2:1. If there are 10 dogs, how many cats are there

Answers

Answer:

10 dogs, 5 cats

Step-by-step explanation:

2:1 = whole to half

Can someone help me m

Answers

The answer is false

Kiran completed x puzzle and Mai completed 3/5 more

Answers

Answer:

why she doing this

Step-by-step explanation:

Tell them that they are slow

The quotient of 4 divided by 1/3 is

4/3
3
12
ASAP pls

Answers

The awnser is 12 ... hope this helpedd

A train leaves the station at time t=0. Traveling at a constant​ speed, the train travels 280 kilometers in 2 hours. Answer parts a and b.

a. Write a function that relates the distance traveled d to the time t.

The function that relates the distance traveled d to the time t is

Answers

Answer:

d = 140t

Step-by-step explanation:

The function that relates the distance travelled d to the time t is d = f(t) = 140t.

What is Speed?

Speed is a scalar quantity which measures the rate of change of the position of an object without measuring on the direction.

In other words, it can be defined as the ratio of distance covered by an object to the time taken by the object to cover the distance.

The train leaves the station at time t = 0.

Distance travelled by the train = 280 kilometers

Time taken to travel the distance = 2 hours

Speed = Distance / Time

           = 280 / 2

           = 140 kilometers/ hour.

Given that train travels at a constant speed.

So for any distance 'd' and the time taken to travel the distance 't',

d / t = 140

d = 140t

d = f(t) = 140t

Hence the distance travelled by the train can be related to the time taken by the function, d = f(t) = 140t

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Sarah drives at a speed of 70 miles per hour how long will it take to drive 385 miles?

Answers

Answer:

5.5 hours

Step-by-step explanation:

For this problem, we have to divide.

[tex]385[/tex] ÷ [tex]70 = 5.5[/tex]

Your answer would be 5.5

The graph shows the number of inches of snow over the course of time.
Which statement is not correct about the relationship shown in the graph?
A It is snowing at a steady rate.
B It is snowing at a rate of inch per hour.
C The amount of snow is proportional to the time.
D The coordinate (2, 1) indicates that it has snowed 2 inches in 1 hour

Answers

Correct OPTIONS:

A It is snowing at a steady rate.

B It is snowing at a rate of ½ inch per hour.

C The amount of snow is proportional to the time.

D The coordinate (2, 1) indicates that it has snowed 2 inches in 1 hour

Answer:

D The coordinate (2, 1) indicates that it has snowed 2 inches in 1 hour

Step-by-step explanation:

Using the graph given, let's analyse each options provided to see which statement is ✅CORRECT or ❌ INCORRECT.

A. "It is snowing at a steady rate."

✅This is CORRECT because a straight line graph has a constant rate of change.

B. "It is snowing at a rate of ½ inch per hour."

✅This is CORRECT, because when x (time in hrs) is 1, y (snow in inches) is ½.

C. "The amount of snow is proportional to the time."

✅This is CORRECT because the line of the graph intercepts the point of origin, (0, 0).

D. "The coordinate (2, 1) indicates that it has snowed 2 inches in 1 hour"

❌This is NOT CORRECT. The coordinate (2, 1) indicates that it has snowed 1 inch in 2 hours rather.

x = 2 => time(hours)

y = 1 => snow(inches)

Determine the equation of the circle graphed below.

Answers

Here you go!! Hope this helps

how to concert 347 to 10​

Answers

Answer:

[tex]340_{10}[/tex]

Step-by-step explanation:

divide a line of 1.8m into three parts in the ratio of 5:7:8​

Answers

Answer:

0.45 m, 0.63 m, 0.72 m

Step-by-step explanation:

Let the three parts of the line be 5x, 7x and 8x

Therefore,

5x + 7x + 8x = 1.8

20x = 1.8

x = 1.8/20

x = 0.09

5x = 5*0.09 = 0.45 m

7x = 7*0.09 = 0.63 m

8x = 8*0.09 = 0.72 m

please solve and give step by step explanation ​

Answers

Answer:

= √b/2a⁴

Step-by-step explanation:

First, we can simplify the ³⁄₁₂ to ¼

Next, we can simplify the a³/a⁵ to a⁻⁸ which is ¹⁄ₐ⁸

Then we can simplify the b²/b to b

Now we should have:

√(b/4a⁸)

= √b/√(4a⁸)

= √b/2a⁴

Select all of the situations which can be represented by the expression 25.75x + 10.
A. Carol has $25.75. She earns $10.00 for each car that she washes.
B. Max has $10.00. He earns $25.75 for every lawn that he mows.
C. Jin buys x postcards for $25.75 each and x keychains for $10.00 each.
D. Sasha sells a scarf for $10.00 and x jackets for $25.75 each.
E. Jon buys 10 toy cars for $25.75 each.

Answers

Answer: 1. no

2. yes

3. no

4. yes

Step-by-step explanation:

The video game Fortnite uses a process called skills- based matchmaking to create games where the people in a match are about even in skill. This is done using a K/D ratio and a percent error interval. One lobby allows for people with a 2.0 K/D and a percent error interval of 18% from the baseline K/D. What is the possible range of player K/Ds that can be in this lobby?​

Answers

Answer:

the K/D range is 22%

Step-by-step explanation:

Show the process to get 3x+2=17

Answers

Answer: 5

Step-by-step explanation:

1. 3x+2=17

2. 3x+2-2=17-2 ( we subtract 2 from both sides)

3. then we simplify 3x=15

4. \frac{3x}{3}=\frac{15}{3} then i divide both sides by 3

5.  and as we simplify, x=5

estimate the quotient


7÷1,611

estimated

Answers

Answer:

The answer is 230.14

Easy long division

Find the indicated angle measures. Then justify each answer.

m angle 1​

Answers

Answer:

m<1 is 115°

This is said to be true by the alternate interior angles theorum which describes this situation

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

alternate interior angles


Can someone give me a step by step explanation because my teacher doesn’t teach us anything? :(

Answers

Answer:

(7x^2 -1)(x - 2).

Step-by-step explanation:

7x^3 - 14x^2 - x + 2

We can factor this by grouping - that is factoring the first 2 terms and the last 2:

= 7x^2(x - 2)  - 1(x - 2)      <-- the x - 2 is common to both parts so we have:

(7x^2 -1)(x - 2).

Find the value of r so the line that passes through each pair of points has the given slope.
Point 1: (-5,r)
Point 2: (1,3)
m = 7/6

Answers

Answer:

- 4

Step-by-step explanation:

( 3 - r ) / ( 1 + 5) = 7/6

[tex]\frac{3-r}{1+5}[/tex] = [tex]\frac{7}{6}[/tex] ⇒ 3 - r = 7 ⇒ r = - 4

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