Check all true statements.
A. For all nonempty sets A, B, C, D, if A x B = C x D, then A = C and B = D.
B. For all sets A, B, the power set of the cartesian product of A and B is the cartesian product of the power sets of A and B. If A={1,2} and B={3} then A x B ={ {1,3}, {2,3} }.
C. The cartesian product has a cancellation property, i.e. if A x B = A x C for some sets A, B, C and A nonempty, then B = C. If A={1,2} and B={3} then A x B ={ (1,3), (2,3) }.
D. The cartesian product is symmetric, i.e. A x B = B x A for all sets A, B. For all sets A, B, the cardinality of A x B is the sum of the cardinalities of A and B.
E. The cartesian product is associative, i.e. (A x B) x C = A x (B x C) =for all sets A, B, C. Both sets are equal to A x B x C.
F. The cartesian product has a cancellation property, i.e. if A x B = A x C for some sets A, B, C, then B = C.

Answers

Answer 1

Step-by-step explanation:

the true statemnts underneath and are in bold letters

-.For all nonempty sets A, B, C, D, if A x B = C x D, then A = C and B = D.

This property is true

-The cartesian product has a cancellation property, i.e. if A x B = A x C for some sets A, B, C and A nonempty, then B = C.

This property is true

- If A={1,2} and B={3} then A x B ={ (1,3), (2,3) }.

if we have 2 non empty sets a and b if we want to get their cartesian product, it is defined as the set of all ordered pairs from a and b

we have A x B to be{(1,3)(2,3)}

therefore this is also true


Related Questions

B is between A and C. AB = 5 and AC = 8. What is the length of BC

Answers

Answer:

BC = 3

Step-by-step explanation:

If you picture A, B, and C on a line, the first part of the line, AB, has a length of 5 and the total line, AC, has a length of 8 . Means that the second part of the line, BC, has a length of 3 because you would add the length of both the first and second part of the line in order to get the total length of the line.

AB + BC = AC

5 + BC = 8

BC = 3

Find the LCM of the given numbers 24 36
A:36
B:72
C:144
D:864

Answers

Answer:

B

Step-by-step explanation:

24*3=72

36*2=72


PLEASE HELP ME
THIS IS DUE IN 10 MINUTES

Answers

Answer:

3rd and 4th one.

Step-by-step explanation:

Can someone please help, ty!!
(Will mark brainliest)

Answers

it should be two hours man

What is 5.5.5 written in exponential form?
A
25
B
53
с
15
D
55

Answers

Answer:

5^3

Step-by-step explanation:

5*5*5

5 multiplied 3 times is

5^3

Answer:

5 ^ 3

Step-by-step explanation:

Write a unit rate for the situations.

30 milliliters every 4 hours

milliliters per hour

Answers

Answer:

[tex]{7.5 \: mm(h)}^{ - 1}[/tex]

Step-by-step explanation:

[tex] a \: unit \: rate \: for \: the \: situations \: is \: given \: by :

\\ rate = \frac{30 milliliters }{ 4 hours} = 7.5\frac{mm}{h} = {7.5 \: mm(h)}^{ - 1} [/tex]

The unit rate for the situation is mL per hour

How do you write a unit rate?An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate. Examples of popular unit rates are the speed in miles per hour, the amount of energy used in miles per gallon, and the speed of the internet in megabits per second. Miles per hour, blinks per second, calories per serving, steps per day, and heartbeats per minute are a few instances of unit rates.

7.5 mL/ hr

The unit rate for the situation is mL per hour

Rate= 30mL/ 4Hrs

Rate= 7.5mL/ hr

To know more about unit rate, refer:

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Y= 4x +3, 4x + y =3 are they parallel or perpendicular

Answers

Answer: Neither

Step-by-step explanation:

When two lines are parallel, their slopes are the same.

When two lines are perpendicular, their slopes are opposite reciprocals. Opposite reciprocals equal -1 when multiplied together.

Equation #1: y = 4x + 3

The equation is in the form y = mx + b, so the slope is 4.

Equation #2: 4x + y = 3

We need to put this equation in slope-intercept form.

1) Subtract 4x from both sides

y = -4x + 3

The slope is -4.

-4 and 4 are neither equal nor opposite reciprocals, so they aren't parallel or perpendicular.

The slope of both lines is neither the same nor negative inverse of each other thus both lines will neither parallel nor perpendicular.

What is slope?

A slope is a tangent or angle at a point or a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

The slope is also calculated by differentiation for example slope of y = sinx will be y' = cosx.

As per the given lines,

y =  4x +3

The slope-intercept form is given as y = mx + c where m is the slope.

By comparing slope m = 4

4x + y =3 → y = -4x + 3

Slope m = -4

Since slopes are not the same thus they will be not parallel.

Perpendicular lines slope's multiplication gives -1.

Since, 4 x (-4) ≠ -1 thus both will be not perpendicular.

Hence "The slope of both lines is neither the same nor negative inverse of each other thus both lines will neither parallel nor perpendicular".

To learn more about slopes,

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If a right triangle has two legs of 7m and 24m what is the length of the longest side? *

Answers

Answer:

It would be 24m

Step-by-step explanation:

The longest side of a right triangle is the hypotenuse.

Use the Pythagorean theorem to solve for the hypotenuse:

X = sqrt(7^2 + 24^2)

X = sqrt( 49 + 576)

X = sqrt(625)

X = 25

The longest side is 25m

Question Help
A local little league has a total of 70 players, of whom 80% are right-handed. How many
right-handed players are there

Answers

Answer:

The number of right-handed people = 56

Step-by-step explanation:

80% of 70 players = number of right-handed people

So, 80/100 x 70 = 56 players

Therefore, number of right-handed players = 56

please help me asap​

Answers

Answer:

11. 6

12. The last option, A=1/4, B=7/16, C=5/8, D=3/4

Step-by-step explanation:

11. look at the denominators, and what do you see? I see that 11 is 88 divided by 8. So, let's divide the numerator by 8 as well! 48/8=6

12. 1/4 is half of 1/2, so it would be between 0 and 1/2, or A

     Same thing with 3/4 but this time in the middle of 1/2 and 1, or D

     5/8 is a little over 4/8, or 1/2, so C

     The last one left is 7/16, B

last week drew worked 7.9 hours. this week he worked 8.6 hours. how many more hours did he work this week than last week?​

Answers

Answer:

0.7 more hours

Step-by-step explanation:

8.6 - 7.9 = 0.7 more hours

0.7 more hours.
8.6-7.9 = 0.7

H(x)=4x+3 what is the coordinate pair for h (1) ?

Answers

Answer:

(1,7)

Step-by-step explanation:

SImply replace x by (1) in the expression to find the value of h:

h(1) = 4 (1) + 3 = 4 + 3 = 7

so for x = 1, h is 7 , which is written as: (1, 7)

A package of 5 pairs of insulated socks costs ​$37.95. What is the unit price of the pairs of socks​?

Answers

Answer:

$7.59.

Step-by-step explanation:

Divide $37.95 dollars (converting it into 37.95), by 5, and you get 7.59 ($7.59).

Answer:

$7.59

Step-by-step explanation:

you dived $37.95 by 5 and you get your answer of $7.59

A pump fills an empty pool at a rate of 500 cubic meters per hour. If one liter is equivalent to one cubic decimeter and 1 meter is equal to 10 decimeters, how many liters of water are in the pool half an hour after the pump starts?

Answers

If a liter equals a cubic decimeter and a meter equals ten decimeters, then 250,000 liters of water is filled in the pool in half an hour.

What is meant by cubic decimeter?

1000 cubic centimeters make up one cubic decimeter. Repeating this procedure would allow us to translate between cubic centimeters and meters or between cubic decimeters and meters. We must keep in mind three conversions. 1000 cubic centimeters is equal to one cubic decimeter.

1 cubic meter = 1000 liters

because, 1 liter = 1 decimeter³

1 meter = 10 decimeters

1 decimeter= 0.1 meters

1 liter = 0.1³ meter³

1 m³ = 1000 liters

Given:

In 1 hour the amount of water filled = 500 cubic meters

In half an hour the amount of water filled = 250 cubic meters

= 250,000 liters.

Therefore, 250,000 liters of water exists filled in the pool in half an hour.

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The Empire State Building is 1,250 feet tall. Maria wants to make a model that has a scale of 1/4 foot = 50 feet. How to tall will her model be?​

Answers

Answer: 25 Feet.

Step-by-step explanation: 1,250 % 50.

help i am stuck look at the image to see but here anyways A teacher is planning a class trip to the aquarium. The aquarium requires two chaperones for every 15 students. The teacher plans accordingly and orders a total of 85 tickets. How many tickets are for chaperones and how many are for students

Answers

75 tickets are for the students and 10 are tickets are for the chaperones

Answer:

Kids- 75

Chaperones- 10

Step-by-step explanation:

We know that the total is 85 tickets. then the aquarium requires 2 chaperones for 15 kids, so you need to do...

15 + 2 = 17

85 / 17 = 5

15 x 5 = 75

2 x 5 = 10

check you work-

75 + 10 = 85

a group of 29 friends gets together to play a sport first people must be divided into teams each has to heve exactly 4 players and no one can be on more than one team how many teams can they make (it is possible that not everyone can be on a team)​

Answers

Answer:

7 groups or teams

Step-by-step explanation:

7 x 4 is 28, as close as we can get to 29.

6.333 x 10^2 standard form

MY BAD!

Answers

Answer:

633.3

Step-by-step explanation:

What does the confidence interval of a confidence level of 99% tell about the population of all college students in the​ state? Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice.

Answers

Answer:

we need to know the options

Step-by-step explanation:

7. Solve the equation using inverse operations. 3 + x = 7
a.
b. x
Il
c. x = 16
d. x = - 16

Answers

X=16...simplify both sides then isolate the variable

Reciprocal of 12 1/3

Answers

Answer:

3 1/12

Step-by-step explanation:

Twelves reciprocal is 1/12 and 1/3s reciprocal is 3.

Answer:

3/37

is your answer

please mark as the brainliest (ㆁωㆁ)

22+33 using GCF and the distributive property.​

Answers

Factors:

22 : 1 2 11 22
33 : 1 3 11 33

Both have the GCF of 11. By removing 11 from both numbers you end up with:

22 = 2 * 11
33 = 3 * 11

Now replace the values on the right of the equals sign into the original equation:

(2 * 11) + ( 3 * 11)

The distributive property allows us to remove the common values and rewrite as:

11(2 + 3)

This gives:

11(5)

55

Translate this sentence into an equation.
57 is the sum of 9 and Diego's height.
Use the variable d to represent Diego's height.

Answers

Answer:

d + 9 = 57

Step-by-step explanation:

If one inch represents 15 feet, what dimensions would you use to make a scale drawing of a building 550 feet by 600 feet?

Answers

9514 1404 393

Answer:

  36 2/3 inches by 40 inches

Step-by-step explanation:

To find the drawing dimension, multiply the actual dimension by the scale factor:

  (550 ft)×(1 in/(15 ft)) = (550/15) in = 36 2/3 in

  (600 ft)×(1 in/(15 ft)) = (600/15) in = 40 in

The dimensions on the drawing would be 36 2/3 inches by 40 inches.

X+4 x+1
Write an equation to determine the value of x so that each pair of polygons has the same perimeter. Then solve

Answers

Answer:

5x i think

Step-by-step explanation:

hopenit is right

I don’t understand this question.

Answers

Angle TQS is equal to 74 degrees
Answer: If the answer to the first angle is 106, the next answer would be 74. This is because the total is 180 because its straight. So, subtract 106 from 180. You get 74.

Explanation: x=7 in this case. When its says, TQS, it means that particular angle.

3(a – 7) = -9 + 3a.

Answers

Answer:

0=12

No Solution

Step-by-step explanation:

Hope this helps (:

Look at the attachment

Please help me fast.

Answers

It is c have a nice rest of your day.

Answer:

26

Step-by-step explanation:

all you have to do is count and add i took the test before

A line with a slope of -10 passes through the point (1,-10) what is it equation in slope intercept form?

Answers

Answer:

y=-10x

Step-by-step explanation:

m=-10

For (1,-10) a=1  AND  b=-10

(use the formula y-b=m(x-a) to find the equation of the line)

y-b=m(x-a)

(sub the values of m (the slope) and a&b (from the point)

y - (-10) = (-10) × ( x - 1 )

(simplify)

y+10=-10(x-1)

(expand the bracket)

y+10=-10x+10

(subtract 10 for both sides)

y=-10x+10-10

(simplify)

y=-10x

PLLLLLLLLZZZZZZZ SOMEONE HELP ME
For a field trip 23 students rode in cars and the rest filled five buses. How many students were in each bus if 288 students were on the trip?

Answers

Answer: First, you start with the equation:

9

x

+

4

=

472

Since four students rode in cars, you want to eliminate this part of the problem to find how many students actually rode in the buses

So you would subtract

4

from both sides and get:

9

x

=

468

Finally, you would divide both sides by

9

and get

52

students on each bus

Step-by-step explanation: First, you start with the equation:

9

x

+

4

=

472

Since four students rode in cars, you want to eliminate this part of the problem to find how many students actually rode in the buses

So you would subtract

4

from both sides and get:

9

x

=

468

Finally, you would divide both sides by

9

and get

52

students on each bus

Other Questions
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