P(A) is the power set of A. Show that-
(i) P(AUB) = P(A) ∩ P(B) is always true, but
(ii) P(AUB) = P(A) U P(B) may not be always true.​

Answers

Answer 1

[tex]\large\underline{\sf{Solution-}}[/tex]

Let assume that,

[tex]\rm \longmapsto\:A \: = \:\{x\} \: [/tex]

and

[tex]\rm \longmapsto\:B \: = \:\{y\} \: [/tex]

[tex]\rm\implies \:A \: \cap \: B = \phi [/tex]

and

[tex]\rm \longmapsto\:A\cup B = \{x, \: y\}[/tex]

We know,

Power set of a set A is defined as set of subsets of A.

So,

[tex]\rm \longmapsto\:P(A) = \{ \phi ,\: x\}[/tex]

and

[tex]\rm \longmapsto\:P(B) = \{ \phi ,\: y\}[/tex]

and

[tex]\rm\implies \:P(A \: \cap \: B) =\{ \phi \}[/tex]

and

[tex]\rm \longmapsto\:P(A\cup B) = \{\phi ,x,y,xy\}[/tex]

Now, Consider

[tex]\rm \longmapsto\:P(A)\cup P(B) = \{\phi ,x,y\}[/tex]

and

[tex]\rm \longmapsto\:P(A\cup B) = \{\phi ,x,y,xy\}[/tex]

[tex]\rm\implies \:\boxed{\tt{ \: P(A)\cup P(B) \: \ne \: P(A\cup B) \: }} \\ [/tex]

Now, Consider

[tex]\rm \longmapsto\:P(A\cap B) = \{\phi \}[/tex]

and

[tex]\rm \longmapsto\:P(A) \: \cap \: P( B) = \{\phi \}[/tex]

[tex]\rm\implies \:\boxed{\tt{ \: P(A)\cap P(B) \: = \: P(A\cap B) \: }} \\ [/tex]


Related Questions

the ratio of yellow balls to green balls in a a bag is 4:2
what faction of the balls are yellow?

Answers

4/6
= 2/3

As we take total and divide by what we looking for

.

Answer: for every 1 green ball there is 2 yellow balls so 75% yellow 25% green I think unless I’m wrong which I wouldn’t be surprised

Step-by-step explanation:

dbtnjjj5ygjhts2hjuuujjhjj​

Answers

Answer:

thanks for the points........

Answer:

wt f ok?

Step-by-step explanation:

A metal strip is being installed around a rectangular workbench that is 8 feet long and 4 feet wide. If the stripping costs ​$4 per​ foot, find the total cost of the stripping.

Answers

Answer:

$144

Step-by-step explanation:

Length*Width*Price

12*3 = 36

36*4 = 144

$144

13 degree difference?

15 degree difference?

16 degree difference?

17 degree difference?

Answers

Answer:

gggggggggggggggvggfggffvvvcvcccccfffcffffffffff

[tex]201[/tex]

whats this i have been struggling for this . 5(3x−2)=−x−10

Answers

Answer:

[tex]x=0[/tex]

Step-by-step explanation:

[tex]5(3x-2)=-x-10~(Given)\\\\15x-10=-x-10~(Distribute~5~to~3x-2)\\\\15x-10+x=-x-10+x~(Add~x~on~both~sides)\\\\16x-10=-10~(Simplify)\\\\16x-10+10=-10+10~(Add~10~on~both~sides)\\\\16x=0~(Simplify)\\\\\frac{16x}{16}=\frac{0}{16}~(Divide~16~on~both~sides)\\\\x=0~(Simplify)[/tex]

lee Hoskins: Attempt 1

A tennis racket with a price of $180 is subject to a sales tax of 7%. What is the total
price of the racket?
$192.60
$187

Answers

I think it is $192.60
7% of 180 is 12.60, then add 12.60 to 180 and you’ll get 192.60!!

[tex]\sf 15=2x-9[/tex]

Answers

Answer:

x=12

Step by step explanation:

Step by step explanation:Add 9 to both sides :

15 = 2x - 9

15 + 9 = 2x - 9 + 9

Simplify:

24 = 2x

Divide both sides to get the result:

24 = 2x

24/2 = (2x)/2

Result:

x=12

[tex]\boxed{\sf Answered \: By\: Subhash} [/tex]

[tex]\boxed{\sf Good\: luck \: for \: your \:assignment} [/tex]

Answer:

x=12

Step-by-step explanation:

[tex]15=2x-9[/tex]

[tex]2x-9=15[/tex]

[tex]2x-9+9=15+9[/tex]

[tex]2x=24[/tex]

[tex]\cfrac{2x}{2}=\cfrac{24}{2}[/tex]

[tex]x=12[/tex]

help ill give brainly

Answers

Answer:

The answer would be 26%

Step-by-step explanation:

Answer:27  

i think that 27 is the answer

Even more picrews of mine............... THIS IS THE LAST ONE I WILL MAKE K? (not to be mean)

i have a lot of picrew

Answers

Answer:

Honestly you should enter the art show or something in your city/country

Step-by-step explanation:

It is good.

Order of operations question

Answers

Answer:

165 po ang sagot

Kung Hindi po tama sorry

I try my best

What is the difference in the account balances shown below? Behrooz: (-$21.00) Cody: $3.00

Answers

Answer:

-7

Step-by-step explanation:

-21.00/3.00

starts at 12 and ends at 6​

Answers

Answer:

126

Step-by-step explanation:

i don't know if it's correct or not

6 hours?
••••••••••••••
probably would be best to give more info

PLSSS HLEPP ME OUTT ITS URGENTTTT​

Answers

Answer:

76 and 19 are the answers

At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $2.40 and the cost of a large greeting card is $3.70. How much would it cost to get 2 small greeting cards and 3 large greeting cards? How much would it cost to get x small greeting cards and y large greeting cards?

Answers

Answer:

1)15.9

depends on what x and y are but put 15.9 ig

Step-by-step explanation:

Answer:

cost of smalls + cost of larges so the answer is 2.40+3.70

Step-by-step explanation:

in a survey 75% of respondents said that they watch TV for one hour each day if 30 respondents said they watch tv for one hour each dat how many respondents took survey in total?

Answers

Answer:

the total number of respondents who took the survey are, 40

Happy To Help :)        Brainlyist Please!

In this question, you 75% is equal to 30.

Cross multiply
(30/75) x (x/100)

(30 x 100) / (x x 75) = 40

40 is the answer

Which of the following values makes the equation
4x − 8 = −4 true?

−3

−1

1

3

Answers

Answer:  C) 1

Work Shown:

4x - 8 = -4

4x = -4+8

4x = 4

x = 4/4

x = 1

To check the answer, we replace x with 1 in the original equation. After simplifying, we should get the same thing on both sides

4x - 8 = -4

4(1) - 8 = -4

4 - 8 = -4

-4 = -4

The answer is confirmed.

true? I believe due to how it starts with positive 4 and is subtracted by -8 this conceding a negative number.

Solve the equation
[tex] \frac{1}{x} + \frac{1}{3x} = 4[/tex]
CORRECT ANSWER+EXPLANATION SHALL BE MARKED BRAINLIEST+35POINTS

thanks xx)​

Answers

pasensya naka limutan kona

Two numbers have a sum of 32. One number is 6 more than the other. Find the numbers

Answers

Answer: 13 & 19

Step-by-step explanation:

Let the bigger number be 'U' and the smaller number 't'.

Since the two numbers have a sum of 32, then   U + t = 32.

& since one number is 6 more than the other, the U - 6 = t

⇒ U + U - 6 = 32

             2U = 38

                U = 19

By substituting fot the value of U we found,

19 - 6 = t

      t  = 13

∴ the numbers are 13 & 19.

Answer:

13 and 19

Step-by-step explanation:

let's first set the two mystery numbers as "x"

and we know that x + (x + 6) = 32 since one of the numbers is 6 more than the other.

now let's set it up:

x + x + 6 = 32

= 2x = 26

= x = 13

so we know that x = 13 now we need to find the other number so we do:

13 + 6 = 19

now to check our work:

13 + 19 = 32

hope that helped :))

Round 848704to the nearest thousand

Answers

Answer:

849000

Step-by-step explanation:

I used a site called Rounding to the Nearest Thousand Calculator. Sorry Brainly doesn't allow links:))) Happy Halloween!!

Andrea drove 20 1/2 miles in 1/3 of an hour at constant speed what was that speed

Answers

Answer:

423

Step-by-step explanation:

123423

The constant speed for the given distance and time is 123/2 miles/hour.

Given that, Andrea drove [tex]20\frac{1}{2}[/tex] miles in 1/3 of an hour at constant speed.

What is the speed?

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Here, [tex]20\frac{1}{2} = \frac{41}{2}[/tex]

Now, speed = Distance ÷ Time

= 41/2 ÷ 1/3

Change division to multiplication and reciprocal the fraction

That is, 41/2 × 3/1

= 123/2 miles/hour

Therefore, the constant speed for the given distance and time is 123/2 miles/hour.

To learn more about the speed, distance, and time visit:

brainly.com/question/4978052.

#SPJ2

5 = t + 12
please help me for this

Answers

Answer:

t = -7

Step-by-step explanation:

You have to get t by itself. Just take the 12 and subtract it from both sides. 5-12 on the left and 12-12 on the right. You then end up with -7 = t or t = -7.

Bertha read 21 books. Each book had 155 pages. How many pages did she read altogether? 465 pages
3,155 pages
3,355 pages
3,255 pages

Answers

21 x 155 = 3255
She read 3255 pages altogether.

Answer:

3,255 pages

Step-by-step explanation:

multiply 155 by 21

pls help fast no randoms

Answers

Answer:

A, D, E

Step-by-step explanation:

Those are your surds because when you square root them they stay in the radical

Answer:

hla shougi

Step-by-step explanation:

Two more than a number is the same as 16 decreased by 6 times the number. Find the number.

Answers

Answer:

X+2=16-6x

X=14-6x

Add 6x on both sides.

7x=14

Divide both sides by 7.

X=2

Someone help me I will mark you as brain

Answers

Answer:

Last one hard to explain

I'm having a bit of trouble finding out how to find the Domain of this function. Help please!

Answers

In general, the domain is the set of all x-values for the graph.  

The issue here is that this isn't the graph of a function.  A function has at most one y-value for each x-value and this graph has an infinite number of y-values for the single x-value of 1.

So, either your teacher is wanting you to say the domain is {1}, because that's the only x-value used by the graph, or they're wanting you to say this is a trick question, because this isn't the graph of a function.

The range is the set of all y-values, which is -9<y<9, but again, do they intend this to be a trick question?

Need help pls pls pls asap pls

Answers

Answer:

C(h) = 1+.25h

Step-by-step explanation:

Total cost = flat fee plus .25 times h  ( where h is the number of hours)

C(h) = 1+.25h

helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

I'm guessing 60km.

Step-by-step explanation:

So per hour,

45km÷3=15km/h

Thereof,

In 4 hours,

15×4=60km.

He will bike 60 km bc in 3 hours was 45 45/3 is 15 so add 15 each hour

i Square = Square Root -1. True or false

Answers

Answering is false I know because I’m smart

Solve to find X. 1/5(x - 2) = 1/10 (x + 6)

Answers

Answer:

x = 10

Step-by-step explanation:

First, distribute:

[tex]\frac{1}{5} x - \frac{2}{5} =\frac{1}{10} x+\frac{6}{10}[/tex]

Next, subtract [tex]\frac{1}{5}x[/tex] from both sides:

[tex]-\frac{2}{5} = \frac{1}{10} x -\frac{1}{5} x+\frac{6}{10}[/tex]

(multiply [tex]\frac{1}{5}x[/tex] by 2 to get common denominator, [tex]\frac{2}{10} x[/tex] )

[tex]-\frac{2}{5} =-\frac{1}{10}x +\frac{6}{10}[/tex]

Next, subtract [tex]\frac{6}{10}[/tex] from both sides:

[tex]-\frac{2}{5} -\frac{6}{10} =-\frac{1}{10} x[/tex]

(multiply [tex]\frac{2}{5}[/tex] by 2 to get common denominator, [tex]\frac{4}{10}[/tex] )

[tex]-\frac{10}{10} =-\frac{1}{10} x[/tex] ⇒ [tex]-1=-\frac{1}{10} x[/tex]

Next, multiply both sides by 10:

[tex]-10=-x[/tex]

FInally, divide both sides by -1:

x = 10

Answer:

Step-by-step explanation:

1/5(x-2) =1/10(x+6)

1/5x-2 = 1/10x+0.6

1/5x+1/10x= 0.6-2

0.2x+0.1x= -1.4

0.3x= -1.4

x= -4.67

x= -4.7

x= -5