Prove De Morgan's law by showing that each side is a subset of the other side by considering x ∈ A⎯⎯⎯ A ¯ ∩ B⎯⎯⎯ B ¯ .
Solution :
We have to prove that [tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex] (De-Morgan's law)
Let [tex]$x \in \bar{A} \cap \bar{B}, $[/tex] then [tex]$x \in \bar{A}$[/tex] and [tex]$x \in \bar{B} $[/tex]
and so [tex]$x \notin \bar{A}$[/tex] and [tex]$x \notin \bar{B} $[/tex].
Thus, [tex]$x \notin A \cup B$[/tex] and so [tex]$x \in \overline{A \cup B}$[/tex]
Hence, [tex]$\bar{A} \cap \bar{B} \subset \overline{A \cup B}$[/tex] .........(1)
Now we will show that [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex]
Let [tex]$x \in \overline{A \cup B}$[/tex] ⇒ [tex]$x \notin A \cup B$[/tex]
Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.
[tex]$x \in \overline{A}$[/tex] and [tex]$x \in \overline{B}$[/tex]
Therefore, [tex]$x \in \overline{A} \cap \overline{B}$[/tex] and we have [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex] .............(2)
From (1) and (2),
[tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex]
Hence proved.
HELPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!
Answer:
Length = 6 inches
1. On a trip to Oregon, Sabrina bought a small stone in
the shape of a square pyramid as a souvenir. Determine
the volume of the stone. Round to the nearest tenth.
V-bh(h)
2 in.
121.5 in.
1.5 in.
Answer:
The answer is "[tex]\bold{1.5\ in^3}[/tex]"
Step-by-step explanation:
Please find the complete question in the attached file.
Given:
[tex]l=1.5 \ in\\\\ w=1.5 \ in\\\\h= 2 \ in\\\\[/tex]
The formula for calculating volume:
[tex]\to V=\frac{lwh}{3}[/tex]
[tex]= \frac{2 \times 1.5 \times 1.5}{3}\\\\=\frac{4.5}{3}\\\\=1.5 \ in^3[/tex]
slope = 1, goes through the point (0,6)
f(x) = 3x + 8
fl-1) = ?
I need this done! Decent amount of points! And chance of Boeing marked brainleist! O:
Answer:63
Step-by-step explanation:
I know this its 63
Answer:
Step-by-step explanation:
a) 21 divided by 3 = 7
answer = 7
b)21+21=42
answer = 2
c) 7+6 = 13
answer = 7
d) I don't know or it could be -8-8= -16 (I am not sure)
e) 3 x 30= 90
answer= 90
f)-7-6 = -13
answer= -13
Amy has 4 pounds of ground pork to make meatballs. She uses 5/8 pound per meatball to make 6 meatballs. How many 1/8 -pound meatballs can amy make with the remaining ?
The boiling point of water is 212 degrees. To make a cup of tea, water is boiled, poured into a mug with tea leaves, and set to steep for 4 minutes. In that time, the temperature of the tea reduces to 115 degrees when it is in a room that is 68 degrees. Write an equation for the cooling curve of the tea in this particular room. Round parameters to the nearest 6th decimal place.
Answer:ugh is there an picture maybe i can understand it better?
Step-by-step explanation:
If using the method of completing the square to solve the quadratic equation
22 + 15x – 11 = 0, which number would have to be added to "complete the
square"?
Answer:
Step-by-step explanation:
Let's solve your equation step-by-step.
22+15x−11=0
Step 1: Simplify both sides of the equation.
22+15x−11=0
22+15x+−11=0
(15x)+(22+−11)=0(Combine Like Terms)
15x+11=0
15x+11=0
Step 2: Subtract 11 from both sides.
15x+11−11=0−11
15x=−11
Step 3: Divide both sides by 15.
15x
15
=
−11
15
x=
−11
15
Answer:
x=
−11
15
using the parent function f(x) = 2^x, write the new function, g(x), that transforms f(x) by shifting 6 units up
Answer:
g(x) = 2^x + 6Step-by-step explanation:
Parent function:
f(x) = 2^xTranslation 6 units up:
g(x) = f(x) + 6or
g(x) = 2^x + 6
Given that R = 6x + 3y
Find y when x = 2 and R = 14
Give your answer as a fraction in its simplest form.
Answer:
y = 2/3
Step-by-step explanation:
14 = 6(2) + 3y
14 = 12 + 3y
2 = 3y
y = 2/3
Write a formulation for the 9th term of the sequence below 5, 15, 45, 135
Answer:
a ^5 = 405
I dont really know the answer
Three times the sum of a number and nine is 12. Find the number.
Answer:
7
Step-by-step explanation:
3x+9=12
3x=21
x=7
Answer:
[tex] - 5[/tex]
Step-by-step explanation:
[tex]3(x + 9) = 12[/tex]
Someone plz help me
Answer:
its the second option thats the answer
What is the value of q in the solution to this system of equations?
2m-5q=8
4m+2q=64
A.4
B.6
C.9
D.14
Answer:
4
Step-by-step explanation:
M,q 14,4
The value of q in the system of equations 2m-5q=8 and 4m+2q=64 is 4 thus option (A) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given system of equations,
2m-5q=8
4m+2q=64
Multiply by 2 into the equation 2m - 5q = 8
4m - 10q = 16
Subtract 4m - 10q = 16 by 4m+2q=64
-10 - 2q = 16 - 64
-12q = -48
q = 4
Hence"The value of q in the system of equations 2m-5q=8 and 4m+2q=64 is 4".
For more about the equation,
brainly.com/question/10413253
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can anyone help with this?
Is 3 a factor of 14t-20?
Yes
No
Answer:
No
Step-by-step explanation:
I dont really know
which of the following is equivalent to (5)^7/3? 5^-4
5^4
^7squroot5^3
^3squroot5^7
Answer:
^7 squroot5^3
Step-by-step explanation:
5x2= 10
7÷ 3= 2.5
Help and please make sure the answer is right? :)
Answer:
8
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
hello again lol
these are alternate interior angles so they are equal
5x + 5 = 45
5x = 40
x = 8
if I had 10 cookies and promised my friend to give them 2 how many cookies will i have
Answer:
8 cookies
Step-by-step explanation:
edit one:the answer was 10 cookies, so please go give the person who said 10 cookies first some thanks/brainliest.
edit two:https://brainly.com/app/profile/31525083 is the user who got it first. Check comment if you are gonna say they didn't.
Answer:
8 cookies
Step-by-step explanation:
Well, we can use simple subtraction to answer this problem. You have 10 cookies, and you give away 2, you need to subtract 10 cookies by 2:
10 - 2 = 8
Therefore, you will have 8 cookies left.
Hope this helps :)
For a theater play, the school sold 120 blue tickets for students and 80 red tickets for adults. What percent of the tickets were sold to students?
Answer:
Step-by-step explanation:
120+80=200 the total number of tickets
120(student tickets) ÷ 200 (total tickets)= .6 =60%
Answer:
bin
Step-by-step explanation:
bghgghhshshsbabbsnajswjjegvrjrjrhrbrhrriritt
Rhonda purchased a pair of shoes for $36
She had to pay 6% extra in sales tax How
much extra did Rhondo have to pay?
Is the triangle a right triangle?use the Pythagorean theorem and its converse to explain why or why not.
Answer:
i believe it is f
Step-by-step explanation:
PLEASE HELP ME
Find the total surface area of the figure shown.
Answer:
I think it's C but I might be
Step-by-step explanation:
The price of a watch was increased by 20% to £198
What was the price before the increase?
the perimeter of a square is 7.2 meters how long is each side ?
Answer:
1.8 meters
Step-by-step explanation:
7.2÷4= 1.8
Answer:
1.8 m
Step-by-step explanation:
let side be 'a'.
perimiter of a square = 4(a)
7.2 = 4(a)
7.2/4 = a
therefore, a = 1.8 m.
Please help me on this!!!!
Answer:
670
Step-by-step explanation:
umm i used a calculator
I need help. I have no idea how to do this!
Answer:
A ≈ 5.1 units²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] × 2 sides × sin (angle between them ) , then
A = 0.5 × 7 × 3 × sin29° ≈ 5.1 units²
A coin is flipped 10 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.
True or False
True
Even though it landed on heads 8/10 times, ther's still a 50% chance that it will land on tails. It doesn't change the percentage of it landing on either side. So in that case, it is true.
Hope this helps!
The statement, A coin is flipped 10 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.
What is probability?The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%.
here, we have,
we know that,
The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.
we have,
When a coin is flipped the probability of getting a heads and a tail is 50%.
Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.
The statement, A coin is flipped 10 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.
Learn more about probability here:
brainly.com/question/30034780
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PLZ HELP ME WITH THIS QUESTION!
Answer:
15
Step-by-step explanation:
Answer:
the answer is 15
Step-by-step explanation: