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.
[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]
Find the slope of the line
(15,18) (6,12)
Answer:
slope = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (15, 18 ) and (x₂, y₂ ) = (6, 12 )
m = [tex]\frac{12-18}{6-15}[/tex] = [tex]\frac{-6}{-9}[/tex] = [tex]\frac{2}{3}[/tex]
Remember, when finding the slope, use this formula: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]
We can start by labeling (15, 18) as [tex]x_{1}[/tex] and [tex]y_{1}[/tex] and (6, 12) as [tex]x_{2}[/tex] and [tex]y_{2}[/tex]. Now, we can plug these number into the formula: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1} }=\frac{12-18}{6-15}=\frac{-6}{-9} =\frac{2}{3}[/tex]
Thus, the slope of the line is [tex]\frac{2}{3}[/tex]. Hope this helps! Let me know if you have any questions related to this problem.
Plz help me with this
Answer:
Your picture is blurred
Step-by-step explanation:
Picture is blurred
Answer:
Ronaldo
Step-by-step explanation:
Please help with this math problem! :)
Answer:
look at the photo..................
Answer:
x = 4.8 , y = 4
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{KJ}{NP}[/tex] = [tex]\frac{KL}{NM}[/tex] , substitute values
[tex]\frac{x}{3}[/tex] = [tex]\frac{8}{5}[/tex] ( cross- multiply )
5x = 24 ( divide both sides by 5 )
x = 4.8
and
[tex]\frac{JL}{PM}[/tex] = [tex]\frac{KL}{NM}[/tex] , that is
[tex]\frac{6.4}{y}[/tex] = [tex]\frac{8}{5}[/tex] ( cross- multiply )
8y = 32 ( divide both sides by 8 )
y = 4
Solve for the value of z.
z=18
3z+4+2z-4+90=180
5z+4-4+90=180
5z+90=180
5z=90
z=18
A.
22 cm
6.5 cm
5 cm
-
Find volume
Answer:
357.5cm³
Step-by-step explanation:
To find the volume of the prism, find the area of the triangle and multiply it by the height
Area of the triangle
a = 1/2 × base × height (of the triangle)a = 1/2 × 22 × 5 = 55cm²Volume of prism
55 × 6.5 = 357.5cm³Answer: 357.5cm³
Hope this helps!
Evaluate the expression when n=6
n² – 5n-2
Answer:
4
Step-by-step explanation:
(6^2) -5(6) -2 =4
that is the answer
Step-by-step explanation:
6^2 - 5×6 - 2
= 36 - 30 -2
= 4
Find the point if intersection of these two lines using algebra.Y= -x+3 and y=3x+2
Answer:
x = 1/4, y = 11/4
Step-by-step explanation:
hope this helps
10.A class consist of 25 boys and 15 girls. A student is to be selected for the social work Find the probability that i)a girl is selected ii) a boy is selected
Step-by-step explanation:
[tex] \sf \pink{ ii) a boy is selected}[/tex]
Answer:
Um Sorry I Didn't Understand
PLEASE SHOW YOUR WORK. ITS FOR A TEST!
–4r – 11 = 4r + 21
Answer:
r = -4
Step-by-step explanation:
-4r - 11 = 4r + 21
-8r - 11 = 21
-8r = 32
r = -4
Hopefully this helps!
Brainliest please?
I hope you can see my question, if you have a phone look at the top for my question. Thank you.
Answer: 10 7/8
Step-by-step explanation: 11 2/8 - 3/8 = 10 7/8
english 3 hhhhhhhhhheeeeeeelllllllllllllllllppppppppppp me
Answer:
the answer is: A
because deduce means to arrive at a fact or conclusion by reasoning.
also because the correct word you would use In option A is reduce.
A function is a relation in which every input has exactly one output.
Which choice represents a function?
CLEAR CHECK
Inputs: negative 4, 5, 8, negative 5. Output: 4, 3, 9, negative 5). Negative 4 goes to 4 and 3. 5 goes to 3. 8 goes to 9. negative 5 goes to negative 5.
On a coordinate plane, a vertical line goes through x = 3.
A 2-column table with 7 rows. Column 1 is labeled x with entries 4, 3, 0, negative 8, 3, 4, 9. Column 2 is labeled y with entries 4, 2, negative 1, 7, negative 3, 5, 14.
(−3,4),(2,6),(0,3),(8,4)
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Answer:
On a coordinate plane, a vertical line goes through x = 3.
Step-by-step explanation:
I haven't looked at the other choices, but clearly this is a function
Answer:
will find at bottom
Step-by-step explanation:
A relation is a function of x if each value of x in the domain corresponds to exactly one value of y in the range. In other words, there should be no repeated values of x with different values of y.
Let's analyze each of the given tables to determine which one represents a function of x:
1. Table 1: In this table, we have x values of -1, 2, 2, and 3. Notice that x = 2 appears twice with different y values. This violates the definition of a function, so Table 1 is not a function of x.
2. Table 2: This table has x values of -8, -8, 1, and 1. Similar to the previous table, x = -8 and x = 1 appear twice with different y values. Therefore, Table 2 is not a function of x.
3. Table 3: In this table, all the x values are the same, which is -5. However, the corresponding y values are different (-9, 7, -9, and 2). Since each x value has a unique y value, Table 3 represents a function of x.
4. Table 4: This table consists of x values of -3, -2, 4, and 7. Each x value corresponds to a unique y value (-1, 5, 0, and -1). Therefore, Table 4 also represents a function of x.
To summarize, the relations that are functions of x are Table 3 and Table 4.
A farmer has a grain bin with 4,000 cubic feet of barley in it. He uses 800 cubic feet to feed his herd of cows. The next day, he buys 800 cubic feet of barley and puts it into the grain bin. How many cubic feet of barley are in the grain bin now?
A) 2,400
B) 4,000
C) 4,800
D) 5,600
Answer:b- 4,000
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
It is B because
4000-800=3200
then
3200+800=4000
so he answer is B.4000
When converting from inches to feet, the measurement in inches, m, of an object varies directly with its measurement in feet, f, with the constant of variation being 12.
What is the equation relating these two quantities?
How many inches would a 3.5-foot object measure?
inches
How many feet would a 27-inch object measure?
Step-by-step explanation:
wow, how complicated can one phrase this ...
the point being :
1 ft = 12 in and vice versa (1 in = 1/12 ft)
so, any measurements given in feet but needed in inches need to be multiplied by 12.
and any measurements given in inches but needed in feet need to be divided by 12.
so,
3.5 ft = 3.5×12 = 7/2 × 12 = 7×6 = 42 in
27 in = 27/12 = 9/4 = 2 1/4 or 2.25 ft
Answer:When converting from inches to feet, the measurement in inches, m, of an object varies directly with its measurement in feet, f, with the constant of variation being 12.
What is the equation relating these two quantities?
✔ m = 12f
How many inches would a 3.5-foot object measure?
✔ 42
inches
How many feet would a 27-inch object measure?
✔ 2.25
feet
Step-by-step explanation:
if you were born 10 years ago how old would you be:
Step-by-step explanation:
Add 10 to the age you are now and get an answer.
Your age will be 10 years old.
What is riddle?A riddle is a statement, question or phrase having a double or veiled meaning, put forth as a puzzle to be solved.
Riddles are of two types: enigmas, which are problems generally expressed in metaphorical or allegorical.
Given that we need to find if you were born 10 years ago how old would you be,
So, you will be 10 years old.
It because when you born 10 years ago, The same as your age.
Thats the puzzle when someone's questions, that called Riddle.
A riddle is a statement, question or phrase having a double or veiled meaning, put forth as a puzzle to be solved.
Hence Your age will be 10 years old.
Learn more about riddles click;
https://brainly.com/question/478260
#SPJ2
The function C(x)=17.5x-10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon. How much does it cost to buy five tickets?
Answer:
8 tickets
Step-by-step explanation:
x = 10 in the given equation.
We have then:
C (x) = 17.5x - 10
C (10) = 17.5 * (10) - 10
C (10) = 165
Answer:
to buy 10 tickets cost:
$ 165
b. How many tickets can you buy with $ 130?
For this case we must make the substitution: C (x) = 130
We have then:
C (x) = 17.5x - 10
130 = 17.5x - 10
Clearing x we have:
17.5x = 130 + 10
17.5x = 140
x = (140) / (17.5)
x = 8
Answer:
You can buy 8 tickets with $ 130
what is 53 + x = x + 53
- BRAINLIEST answerer
Which of the following ratios are equivalent to the ratio 8 : 7?
Answer: 0.875 or 56/49
Step-by-step explanation:
A quality manager for a publishing company checks 3 of every 250 books printed for typos. At that rate, how many of every 15,000 books will be checked for typos?
Answer:
Print between 25 - 2,000 books. Your price per book will go down as your quantity increases.
Step-by-step explanation:
A translation 2 units to the right and 10 units up. Then a reflection over the line AC
pls help me im confused will give brainliest
Answer:
dffffgggggghhhhhhhh give me my points
Step-by-step explanation:
why dose it not telling me the ansewr
Answer:
I don't know ::{
Step-by-step explanation:
Help Pleasseeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
graph points (0,2) and (0.857,0)
Step-by-step explanation:
can i please have the brainliest
One of Kylie's homework problems is to convert 30 centimeters to feet, given that 2.54 centimeters = 1 inch. Here is her
work:
30 centimeters
2.54 centimeters 12 inches
= 30 x 254x12=914 4 feet
1 inch 1 foot
Which of the following statements is true?
Kylie's conversion is correct
Kylie's conversion is incorrect because she set up the conversion ratios incorrectly.
Kylie's conversion is incorrect because she multiplied incorrectly
Kylie's conversion is incorrect because her conversion ratios are not equivalent to 1.
Answer:
She set up the conversion ratios incorrectly.
Step-by-step explanation:
30 cms
= 30 / 2.54 inches
= 30 / 2.54 / 12feet
= 0.984 feet.
Please help!! Will mark brainliest!
What are the domain and range of each relation?
Drag the answer into the box to match each relation.
Answer:
-2,-4
0,-4
-1,-2
-1,2
2,2
Step-by-step explanation:
on the left is the x which is domain and on the right is the y which is range so connect the lines and get ur answer
Please help me out. Last question I have to finish !!!
105 people
I hope this helps I would appreciate brainliest if possible :)
Answer:
okay so 105 x 37 = 3885 + 80 + 3965 Which is the max within there budget
Step-by-step explanation:
so your answer is 105
What is the value of this
Answer: -16 Happy to Help :) Brainliest Please
Step-by-step explanation:
Answer:
-16
Step-by-step explanation:
On a certain hot summer's day, 557 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totalled $1146.75. How many children and how many adults swam at the public pool that day?
Answer:
Adults:193
children:295
Two numbers are co-prime if they have no common factors (other than
1). By drawing Venn diagrams or otherwise, decide whether each pair of
numbers is co- prime.
a) 105 and 429 b) 63 and 715 C) 121 and 175 d) 455 and 693
Answer:
See below.
Step-by-step explanation:
a)
105/3 = 35
35/5 = 7
7/7 = 1
429/3 = 143
143/11 = 13
13/13 = 1
105 = 3 * 5 * 7
429 = 3 * 11 * 13
Not co-prime
For the other parts of the problem, do the same I did above. Find the prime factorizations of both numbers, and see if they have any prime factors in common.