Answer:
Where is the graph???
Step-by-step explanation:
Which of the following statements is true for all sets A,B and C? Give a proof
or a counter example.
(a) A ⊆ ((A∩B)∪C).
(b) (A∪B)∩C = (A∩B)∪C.
(c) (A\B)∩C = (A∩C) \ (B∩C).
Answer:
(a) and (b) are not true in general. Refer to the explanations below for counterexamples.
It can be shown that (c) is indeed true.
Step-by-step explanation:
This explanation will use a lot of empty sets [tex]\phi[/tex] just to keep the counterexamples simple.
(a)Note that [tex]A \cap B[/tex] can well be smaller than [tex]A[/tex]. It should be alarming that the question is claiming [tex]A\![/tex] to be a subset of something that can be smaller than [tex]\! A[/tex]. Here's a counterexample that dramatize this observation:
Consider:
[tex]A = \left\lbrace 1 \right\rbrace[/tex].[tex]B = \phi[/tex] (an empty set, same as [tex]\left\lbrace \right\rbrace[/tex].)[tex]C = \phi[/tex] (another empty set.)The intersection of an empty set with another set should still be an empty set:
[tex]A \cap B = \left\lbrace 1\right\rbrace \cap \left\lbrace\right\rbrace = \left\lbrace\right\rbrace[/tex].
The union of two empty sets should also be an empty set:
[tex]((A \cap B) \cup C) = \left\lbrace\right\rbrace \cup \left\lbrace\right\rbrace = \left\lbrace\right\rbrace[/tex].
Apparently, the one-element set [tex]A = \left\lbrace 1 \right\rbrace[/tex] isn't a subset of an empty set. [tex]A \not \subseteq ((A\cap B) \cup C)[/tex]. Contradiction.
(b)Consider the same counterexample
[tex]A = \left\lbrace 1 \right\rbrace[/tex].[tex]B = \phi[/tex] (an empty set, same as [tex]\left\lbrace \right\rbrace[/tex].)[tex]C = \left\lbrace 2 \right\rbrace[/tex] (another empty set.)Left-hand side:
[tex](A \cup B) \cap C = \left(\left\lbrace 1 \right\rbrace \cup \left\lbrace \right\rbrace\right) \cap \left\lbrace 2 \right\rbrace\right = \left\lbrace 1 \right\rbrace \cap \left\lbrace 2 \right\rbrace = \left\lbrace \right\rbrace[/tex].
Right-hand side:
[tex](A \cap B) \cup C = \left(\left\lbrace 1 \right\rbrace \cap \left\lbrace \right\rbrace\right) \cup \left\lbrace 2 \right\rbrace\right = \left\lbrace \right\rbrace \cup \left\lbrace 2 \right\rbrace = \left\lbrace 2 \right\rbrace[/tex].
Apparently, the empty set on the left-hand side [tex]\left\lbrace \right\rbrace[/tex] is not the same as the [tex]\left\lbrace 2 \right\rbrace[/tex] on the right-hand side. Contradiction.
(c)Part one: show that left-hand side is a subset of the right-hand side.
Let [tex]x[/tex] be a member of the set on the left-hand side.
[tex]x \in (A \backslash B) \cap C[/tex].
[tex]\implies x\in A \backslash B[/tex] and [tex]x \in C[/tex] (the right arrow here reads "implies".)
[tex]\implies x \in A[/tex] and [tex]x \not\in B[/tex] and [tex]x \in C[/tex].
[tex]\implies (x \in A\cap C)[/tex] and [tex]x \not\in B \cap C[/tex].
[tex]\implies x \in (A \cap C) \backslash (B \cap C)[/tex].
Note that [tex]x \in (A \backslash B) \cap C[/tex] (set on the left-hand side) implies that [tex]x \in (A \cap C) \backslash (B \cap C)[/tex] (set on the right-hand side.)
Therefore:
[tex](A \backslash B) \cap C \subseteq (A \cap C) \backslash (B \cap C)[/tex].
Part two: show that the right-hand side is a subset of the left-hand side. This part is slightly more involved than the first part.
Let [tex]x[/tex] be a member of the set on the right-hand side.
[tex]x \in (A \cap C) \backslash (B \cap C)[/tex].
[tex]\implies x \in A \cap C[/tex] and [tex]x \not\in B \cap C[/tex].
Note that [tex]x \not\in B \cap C[/tex] is equivalent to:
[tex]x \not \in B[/tex], OR[tex]x \not\in C[/tex], ORboth [tex]x \not\in B[/tex] AND [tex]x \not \in C[/tex].However, [tex]x \in A \cap C[/tex] implies that [tex]x \in A[/tex] AND [tex]x \in C[/tex].
The fact that [tex]x \in C[/tex] means that the only possibility that [tex]x \not\in B \cap C[/tex] is [tex]x \not \in B[/tex].
To reiterate: if [tex]x \not \in C[/tex], then the assumption that [tex]x \in A \cap C[/tex] would not be true any more. Therefore, the only possibility is that [tex]x \not \in B[/tex].
Therefore, [tex]x \in (A \backslash B)\cap C[/tex].
In other words, [tex]x \in (A \cap C) \backslash (B \cap C) \implies x \in (A \backslash B)\cap C[/tex].
[tex](A \cap C) \backslash (B \cap C) \subseteq (A \backslash B)\cap C[/tex].
Combine these two parts to obtain: [tex](A \backslash B) \cap C = (A \cap C) \backslash (B \cap C)[/tex].
what is d divided by equals
Answer: X and Y
Step-by-step explanation: IF I REMEMBER dont get mad if you don’t get it right
what are the two characteristics we look for when trying to solve a quadratic equation?
A. A positive coefficient for x^2 & the equation set equal to 0
B. Factor and cancel
C. Distribute like terms
D. There is no such thing as a quadratic equation
Answer:
Answer A makes the most sense by far.
Step-by-step explanation:
Answer A makes the most sense by far. However, strictly speaking, the coefficient of x^2 does not have to be positive if we're using the quadratic formula. Using some other approach, such as factoring, obtaining a positive coefficient for x^2 is helpful.
Graph the line with this equation.
y= 2x + 2
Answer: it would be 2 to the right and 2 up
Step-by-step explanation:
2 right 2 up
ent
Use the interactive to find an expression equivalent to
4x - 4 - 2x + 3.
O 2x - 1
O 6x - 1
O 2x - 7
O-2x + 3
Please hurry help
Answer:
it's A
Step-by-step explanation:
2x - 1
I put b and got it wrong
Use the factor theorem to determine which of the following is a factor of f(x)=x^3+5x2-15x+9
x-2
x+1
x-1
x+2
show work please
x+2
Step-by-step explanation:
x+2
If x = –2 is a zero, then x + 2 = 0, so x + 2 is a factor. Similarly, if x = 1/3 is a zero, then x – 1/3 = 0, so x – 1/3 is a factor. By giving me two of the zeroes, they have also given me two factors: x + 2 and x – 1/3.
can someone help me please
Answer:
2,5,8,11,14,17,20
Description: Each time there was an addition of 3 onto each 'y'.
Step-by-step explanation:
+3 to the last one each time
2+3=5
5+3=8 etc
Determine the intercepts of the line
X-intercept: (__ , __)
Y-intercept: (__, __)
16x2 - 8x + 1 is an example of a ______
Answer:
the answer would be an equation
Write an equation in slope-intercept form for the line that passes through (1,-2) and (3, 7)
Answer:
y=9/2x -13/2
Step-by-step explanation:
i used a calculator i hope its right
Please help!!!
is a relation that is also a function.
Answer:
Step-by-step explanation:
If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
is there a way you guys can show me how to graph this equation? if not something will do
Answer:
you can use an online graphing calculator
Step-by-step explanation:
Use the link in the screenshot
btw, the line after the word calculator is the cursor, so don't put anything after the word calculator.
A study was conducted to analyze the amount of time spent sitting at a desk for employees over a work day. The time spent sitting was recorded for a large sample of employees and found to follow a bell-shaped distribution with a mean of about 280 minutes. The smallest amount of time was 100 minutes and the largest amount of time was 460 minutes. Unfortunately, the standard deviation was not reported in the summary. Which of the following represent the most appropriate value for that standard deviation?
A. Options 60 minutes
B. 90 minutes
C. 180 minutes
D. 360 minutes
Please help with the question, and if you can please explain how you got the answer. Thank you.
9514 1404 393
Answer:
C. p ∨ q
Step-by-step explanation:
The compound statement is of the form ...
p or q
where ...
p = Memorial day is in July
q = parallel lines intersect
The symbol ∨ is used to represent the disjunction (or).
The symbolic form of the given statement is ...
p ∨ q
__
As it happens, both p and q are false, which means the disjunction is false. That has no bearing on the symbolic representation of it.
_____
∧ represents conjunction (and).
Are these relations functions?
Answer:
Letter B is yes because if you use the vertical line test, never anytime the vertical line intersect the graph in more than one point.
Solve the following inequality -9/2x grater then or equal to -1/4
Answer:
Did you mean [tex]\frac{-2x}{9} ?\\[/tex]
Please clarify so that I can work this problem out for you :)
Step-by-step explanation:
How do you solve -2 1/2+3/4÷3/8
Step-by-step explanation:
1. use PEMDAS (Parentheses, Exponent, Multiplication & Division, Addition & Subtraction). you would do 3/4 divided by 3/8 first.
3/4 / 3/8 = 2
2. add 2 to -2 1/2 (or if it's easier to understand, do 2 minus 2 1/2)
-2 1/2 + 2 = -1/2 OR 2- 2 1/2 = -1/2
answer is -1/2
Find the slope......
Answer:
Step-by-step explanation:
5. A boat traveled 27 miles in 2 hours. At this rate, how many miles will the boat travel in 4 hours?
What is the estimated age of Earth?
Answer:
4.543 billion years i think, i apologize if im wrong
Step-by-step explanation:
Answer:
4.54 billion years
Step-by-step explanation:
Scientists use the layers of rock of the Earth's crust/core to estimate how old is the earth.
How do you subtract an integer from another integer without using
number line? Give an example.
a
Answer:
9-8=1
7-(-6)=13
Step-by-step explanation:
you just add it the normal way.
Answer:
See below
Step-by-step explanation:
See following examples
a and b
a- ba and -b
a - (-b) = a + b-a and b
-a - b = -(a + b)-a and - b
-a - (-b) = -a + b = b - aA researcher is testing the claim that the average university student works less then 15 hours a week. To test this claim she surveys a random sample of 20 undergraduate students who reported an average of 13.5 hours a week of work. We will assume that the population is normally distributed with a standard deviation of 5 hours per week.
Test this claim at the alpha of 0.02 by calculating the z-score and comparing it to the critical z-score (z subscript c r i t end subscript equals negative 2.05 right parenthesis.
You have the standard error of the mean, so solve for the z-score.
Answer:
no
Step-by-step explanation: pick up the phone baby i know your home
Hanna is recovering hundreds of treasure chests from an ancient shipwreck. She is able to recover 8 chests
every 4 hours.
Complete the table using equivalent ratios.
Treasure chests
Hours
8
4
6
10
What is the Scale Factor going from the larger figure to the smaller figure?
Answer:
0.25
Step-by-step explanation:
scale factor=md/od
=0.5/2
0.25
How to solve ?? 3 (3z-6)=0
Answer:
Step-by-step explanation:
3(3z-6)=0
multiply your three with the 3z and the -6
9z-18=0
figure out what - 18 = 0
9z=18
9*2=18
z=2
hope this helps
whats 9×9 how do you get the answer
Answer:
9 × 9 = 81
This is basic 12x12 tables math
Answer:
81
Step-by-step explanation:
you just take 9 and times it by 8 and you get 81
If the planes extend infinitely in all directions, where do plane ADB and line EC intersect?
Answer: In point C.
Step-by-step explanation:
Plane ADB is the plane that contains the points A, D and B.
If you look in the image, you can see that point C also does belong to this plane.
Line EC is the line that connects the points E and C.
Now, remember that Point C does belong to the plane ADB, then the point where the plane ADB and line EC intersect is in point C, because it is a common point to both elements.
527 x 36
What will this equal
Answer:
18972 I use an calculator
The solution of number 527 × 36 after multiplying is,
⇒ 527 × 36 = 18,972
We have to give that,
To solve the expression,
⇒ 527 × 36
Now, simplify the numbers as,
⇒ 527 × 36
After multiply,
⇒ 18,972
So, the solution is,
⇒ 18,972
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ6
HELP WILL GIVE BRAINLIEST to best answer
Answer:
A,B,C,D
Step-by-step explanation:
They are all the same equation on both sides of the equal sign and sense the variable is x on all of them whatever number you put on one side you have to put it on the other side therefore resulting in any solution you could think of.
Plz help I have this and i am being timed
Answer:
i think it is -1/2
Answer:
[tex] -\dfrac{13}{18} [/tex]
Step-by-step explanation:
[tex] -\dfrac{8}{9} - (-\dfrac{1}{6}) = [/tex]
[tex] = -\dfrac{8}{9} + \dfrac{1}{6} [/tex]
[tex] = -\dfrac{16}{18} + \dfrac{3}{18} [/tex]
[tex] = -\dfrac{13}{18} [/tex]
