Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of a quantifier. Next, express the negation in simple English. In each case, identify the domain and specify the predicates.

a. No one has lost more than one thousand dollars playing the lottery.
b. There is a student in this class who has chatted with exactly one other student.
c. No student in this class has sent e-mail to exactly two other students in this class.
d. One student has solved every exercise in this book.
e. No student has solved at least one exercise in every section of this book.

Answers

Answer 1

Answer and Step-by-step explanation:

Not p = ¬p

P or q = p ∨ q  

P and q = p ∧ q

If p then q = p → q

P if and only if q = p ↔ q

Existential quantification:  There exist an element x in the domain such that p(x).

Universal quantification: p(x) for all values of x in the domain.

(a)  No one has lost more than one thousand dollars playing the lottery.

Let A(x) means ‘x has lost more than one dollars playing the lottery’

It can also write as “there does not exists a person that lost more than one thousand dollars playing”

                     ¬Ǝ x A (x)

Negation of this statement:  

By using double negation law:

                               ¬ [¬Ǝ x A (x)]  ≡ Ǝ x A(x)

(b) There is a student in this class who has chatted with exactly one other student.

Let B(x,y) means “ x has chatted with y” and domain is all students of this class.

We can write the given sentence as:

“There is a student in the class who has chatted with one student and this student is not himself and for all people the student chatted with, this student has to be himself or the one student he chatted with”

Ǝ x Ǝ y[B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x,y) → ( z = x v z = y))]

The negation:

               ¬ Ǝ x Ǝ y[B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x ,y) → ( z = x v z = y))]

By using De Morgan’s law for quantifiers:

≡∀x ¬ Ǝ y [B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x ,y) → ( z = x v z = y))]

≡∀x ∀ y [B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x ,y) → ( z = x v z = y))]

De Morgan’s law:

≡∀x ∀ y [¬  B ( x, y) v  ¬ ( x ≠ y) v ∀ z (B(x ,y) → ( z = x v z = y))]

By using De Morgan’s law for quantifiers:

≡∀x ∀ y [¬  B ( x, y) v  x=  y  v Ǝ z¬ (B(x ,z) → ( z = x v z = y))]

(c)  No student in this class has sent e-mail to exactly two other students in this class

Let c(x, y) means “ x has sent email to y” and the domain is all student of class.

Using double negation law:

Ǝ x Ǝ y Ǝ z [c(x, y) ∧c(x ,z) ∧ x≠ y ∧ x ≠z ∧ y ≠ z ∀ w (c(x,w) → ( w = x v w = y v w = z)]

There is a student in class that has sent email to exaxtly two other students in class.

(d)  One student has solved every exercise in this book

Let D(x , y) mean student x has solved exercise y in this book.

The negation:  

Ǝx∀yD(x,y)

Use De Morgan’s law for qualifiers:

    ≡∀ x Ǝ y ¬D(x, y)  

(e). No student has solved at least one exercise in every section of this book.

Let E(x, y,z) be student x has solved exercise y in section z of this book.

We can write “there does not exist a student that solved at least one exercise in all sections of this book”

¬Ǝ x Ǝ y ∀ Z E(x, y, z)  

Negation:

                      ≡¬ [¬ Ǝ x Ǝ y ∀ Z E(x, y, z)  ]

Use double negation law:

                                     ≡ Ǝ x Ǝ y ∀ Z E(x, y, z)  


Related Questions

Consider the diagram.
What is the length of segment AB?
A) 7
B) 9
C) 18
D) 25

Answers

Answer:

the answer is 9

Step-by-step explanation:

Answer: the correct answer is 9!!!!!

Last week, Tanya had $43 in her checking
account. She deposited $50 and wrote a check
for $92. How much money is left in her account?

Answers

Answer:

She would have $1 left in her account.

Step-by-step explanation:

43 + 50 = 93

93 - 92 = 1

Hope this helps..?

Answer:

$1

Step-by-step explanation:

We start off with $43.

Tanya deposits $50 to her account.

50+43=93.

She has $93 now.

She writes a check for $92.

93-92=1.

Man, Tanya is broke no cap.

PLEASE HELP!!!
There are 800 students who attend Park Middle School. There are 1.5 times as many boys as there are girls. Assign variables to the unknowns.

Answers

800= 1.5x +y
X is boys
And y are girls

PLEASE HELP BEFORE 4 PM!!!

1. 641 divided by 43
2. 4684 divided by 27
3. 6455 divided by 64

Answers

Answer:

1. Its about 14.90697674418605. I’m not sure if u want it rounded up if u want it rounded up to the nearest whole it would be 15 if I wanted it rounded up to the nearest tenth then it would be 14.9

2. It’s about 173.4814814814815. I wasn’t sure if I wanted this one rounded up too. Rounded up to the nearest whole it would be 173 and rounded up to the nearest tenth it would be 173.5

3. It’s about 100.859375. I wasn’t sure on this one too. Rounded up to the nearest whole would be 101 and rounded up to the nearest tenth it would be 100.9

Step-by-step explanation:

The neighborhood swimming pool drains at a rate of 99 gallons every 3 hours. At this rate, how many gallons are
emptied each hour?
Helllllpppppp meeee

Answers

Answer:

33mph

Step-by-step explanation:

because if u divide 99 by 3 that is the answer


Point M (-3, 6) and point 'N (1,-1) are located on a coordinate
grid.
HURRY!!! PLEASE I WILL GIVE BRAINLIEST!!

Answers

The distance between point M and point is is about 8.06 units (rounded to nearest hundredth)

you just purchased a new hooded sweatshirt for $24. the total cleaning cost is $2 total because it will be washed with other sweatshirts. you will wear the sweatshirt 18 times this winter. calculate the cost per wearing.

Answers

Answer:

Step-by-step explanation:

espera y termino y te ayudo vale que me falta poco vale

If A is the least common multiple of 12, 24, and 36, and B
is the lowest prime number, what is the sum of A and B ?

F.
3
G.
4
H.
73
J.
74
K.
145

Answers

Answer:

74

Step-by-step explanation:

A= Least common multiple of 12,24,36

Factors of 12 = 2*2*3

Factors of 24 = 2*2*2*3

Factors of 36 = 2*2*3*3

A = 2*2*2*3*3 = 72

B = Lowest prime number = 2

A+B = 72+2 = 74

if 6 pounds of apples cost $9, how much would 21 apples cost?​

Answers

31.5 dollars
Explanation:
You can do 6+6 3 time and that equals 27 dollars, and you have one more so 9 divided by 2 is 4.5 so if you add that you get 31.5

Find the midpoint of the segment with the following endpoints.
(3,0) and (0, –8)

Answers

Point 1 ( XA , YA ) = ( 3,0)
Point 2 ( XB , YB) = (0 , -8 )

Solution :

Midpoint ( XM, YM)

= ( XA + XB/2 , YA + Y1/2 )
= ( 3+0/2 , 0-8/2)
= ( 3/2 , -4 )
= ( 1.5 , -4 )

Midpoint of a line segment:
(XM , YM ) = ( 1.5 , -4 )

THE ANSWER IS: 1.5 , -4 ✅

If the absolute value of x is 4, what is the value of x?

A) -16 or 16
B) -4
C) -4 or 4
D) 4

Answers

X = -4 or 4. :)))))))

the correct answer is option C) - 4 or 4.

If the absolute value of x is 4,

| x | = 4

it means that x can be either positive or negative, but its distance from zero is 4 units.

This indicates that x can be 4 units to the right of zero or 4 units to the left of zero.

x = ± 4

Therefore, the possible values of x are - 4 and 4.

Thus, the correct answer is option C) - 4 or 4.

Both - 4 and 4 have an absolute value of 4, fulfilling the condition specified in the problem statement.

Learn more about absolute value here

https://brainly.com/question/17360689

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what is the population of A politician is interested in the proportion of voters in his district who think he is doing a good job. Define the following in terms of the study. Give examples where appropriate.

Answers

Answer:

lovely peachlings

Step-by-step explanation:

what is 1x7791789x79188037891883+8904781982994

Answers

Answer:

6.17016491E20

Step-by-step explanation:

6.170164915E20
This is wild but it’s what my calculator says

What is equal to d? I’m sorry but I need help.

Answers

answer: -9/13

(picture below shows how to solve it)

Simplify each of the following powers of i.
i^99

Answers

Answer:

i= sqrt (-1)

If the power is

- even then the value could be -1 or 1

-odd then the value could be -i or i

99 is odd so now is

-i if (99+1)/2 is even or is

i is (99+1)/2 is odd

Now check (99+1)/2= 100/2= 50,

50 is even so

i^99 = -i

Step-by-step explanation:

Give the person brainliest

The mean of 7 numbers is 29. What is the total of the 7 numbers​

Answers

Answer:

203

Step-by-step explanation:

Multiply the mean by the amount of numbers (7).

find the value of x
The answer is 150.
I need to show my work.

THANKSSSS

Answers

Answer:

x = 150

Step-by-step explanation:

We know a circle is 360°, so the angles must add up to 60°.

Step 1: Set up equation

x - 120 + x - 120 = 60

Step 2: Solve for x

Combine like terms: 2x - 240 = 60Add 240 on both sides: 2x = 300Divide both sides by 2: x = 150

Step 3: Check

Plug in x to verify it is correct.

150 - 120 = 30°

150 - 120 = 30°

30° + 30° = 60°

60° + 300° = 360°

A ball is thrown from the top row of seats in a stadium. The function h(t) = −16t2 + 64t + 80 gives the height, h, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?

Answers

Answer:

Step-by-step explanation:

Given the height of the ball expressed as:

h(t) = −16t^2 + 64t + 80

The ball hits the ground the when h(t) = 0

Substitute h(t) = 0 and find t as shown:

h(t) = −16t^2 + 64t + 80

0 = −16t^2 + 64t + 80

−16t^2 + 64t + 80 = 0

Divide throigh by -16

t^2-4t-5 = 0

t^2-5t+t-5 = 0

t(t-5)+1(t-5) = 0

(t+1)(t-5)= 0

t+1 = 0 and t - 5 = 0

t = -1 and t = 5

time can not be negative:

t = 5seconds

Hence it will take 5 secs before the ball his the ground

Solving a quadratic equation, it is found that the ball hits the ground after 5 seconds.

The height of a ball after t seconds is given by:

[tex]h(t) = -16t^2 + 64t + 80[/tex]

It hits the ground at the values of t for which:

[tex]h(t) = 0[/tex]

Then

[tex]-16t^2 + 64t + 80 = 0[/tex]

Simplifying by -16:

[tex]t^2 - 4t - 5 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 1, b = -4, c = -5[/tex].

Then:

[tex]\Delta = (-4)^2 - 4(1)(-5) = 36[/tex]

[tex]x_{1} = \frac{-(-4) + \sqrt{36}}{2} = 5[/tex]

[tex]x_{2} = \frac{-(-4) - \sqrt{36}}{2} = -1[/tex]  

We want the positive value, thus, the ball hits the ground after 5 seconds.

A similar problem is given at https://brainly.com/question/24764843

I need help in math please I am not able to figure these out, I will give you the brainlest and thank you.

Answers

Answer:

A. -7 A2. -7

B.-14 B2. 2

C.-14 C2.14

D. 1 D2. -7

9514 1404 393

Answer:

  a. -7, -7

  b. -14, 2

  c. -14, -14

  d. 1, -1

  e. misuse of the associative property leads to different results

Step-by-step explanation:

Your calculator (or a spreadsheet) can figure these easily.

a. -12 +(-4 +9) = 12 +5 = -7

  (-12 +(-4)) +9 = -16 +9 = -7

__

b. (14 -20) -8 = -6 -8 = -14

  14 -(20 -8) = 14 -12 = 2

__

c. (14 +(-20)) +(-8) = -6 -8 = -14

  14 +(-20 +(-8)) = 14 +(-28) = -14

__

d. -1 -(-1 +(-1)) = -1 -(-2) = -1 +2 = 1

  (-1 -(-1)) +(-1) = (-1+1) -1 = 0 -1 = -1

__

e. The associative property works for addition. When the associative property is used to rearrange subtraction problems, the minus signs need to be kept with the numbers, as in (c). That is, the problem needs to be expressed as a sum of signed numbers.

In (d), the term -(-1 +(-1)) was broken in the middle when the sum was rearranged for the second expression. Only terms in the same level of parentheses can be rearranged by the associative property.

A one dimensional object with no endpoint is a?
A.ray
B.line segment
C.line
D.point

Answers

Answer:

its line fjfjfjjejjdjdj

As per the given condition, the required one dimensional object with no end point is a line.

What is a ray?

"In geometry, a ray can be defined as a part of a line that has a fixed starting point but no end point. It can extend infinitely in one direction.

On its way to infinity, a ray may pass through more than one point. When naming a ray, it is denoted by drawing a small ray on top of the name of the ray. "

What is a line segment?

"A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints."

What is a line?

"A line is a one-dimensional object, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. "

What is a point?

"A point is a primitive notion that models an exact location in the space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space."

Given, a one dimensional object with no endpoint.

Therefore, the require object is a line.

Learn more about a line here: https://brainly.com/question/27560536

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What are the terms on the expression 2x-4y+8

Answers

the andwer is 2x and -4y

On a family road trip, Mr. Peters travels 130
miles in 2 hours. At this rate, how many miles
will he travel in 7 hours?

Answers

He will travel 455 miles because he travels 65 miles per hour

Fiecare dintre cei 180 de elevi ai unei școli vorbește cel puțin una dintre limbile germană și engleză . Dintre aceștia, 92 vorbesc limba germană și 130 vorbesc limba engleză. *
Numărul elevilor care vorbesc ambele limbi sunt in numar de
Elevii care vorbesc numai germana sunt în număr de
Elevii care vorbesc numai engleza sunt în număr de

Answers

Wlsloadniednheudbeid


Solve the equation for g:
3f+2g = 7h


Will give 69 pts

Answers

Answer:

Step-by-step explanation:

2g=7h-3f

g=[tex]\frac{7h-3f}{2}[/tex]

Answer:

g= [tex]g=\frac{7}{2}h- \frac{3}{2}f[/tex], f∈R, h∈R

Step-by-step explanation:

3f+2g=7h

2g=7h-3f

g=[tex]\frac{7}{2}h - \frac{3}{2} f[/tex]

2. Choose all numbers that are RATIONAL. *
1. 0
2. 5/7
3. 3.6820350285........
4. -10​

Answers

Answer:

0, 5/7, and -10 are RATIONAL numbers ⇒ 1, 2, 4

Step-by-step explanation:

Rational number are the numbers can be written in the form of the fraction [tex]\frac{a}{b}[/tex] , b ≠ 0

Example:

5, -3, 5.2 , -10.567, [tex]2\frac{1}{3}[/tex] , [tex]\sqrt{64}[/tex] , [tex]-\sqrt{\frac{25}{4}}[/tex] , [tex]\frac{\sqrt[3]{8}}{5}[/tex] , .......5 can be written as [tex]\frac{5}{1}[/tex]-3 can be written as [tex]-\frac{3}{1}[/tex]5.2 can be written as [tex]\frac{52}{10}[/tex]-10.567 can be written as [tex]-\frac{10567}{1000}[/tex][tex]2\frac{1}{3}[/tex]  can be written as [tex]\frac{7}{3}[/tex][tex]\sqrt{64}[/tex] can be written as [tex]\frac{8}{1}[/tex][tex]-\sqrt{\frac{25}{4}}[/tex] can be written as [tex]-\frac{5}{2}[/tex] [tex]\frac{\sqrt[3]{8}}{5}[/tex] can be written as [tex]\frac{2}{5}[/tex]

All the numbers above are rational numbers

Let us find the rational numbers in our question

∵ 0 can be written as [tex]\frac{0}{1}[/tex]

0 is a rational number

∵ [tex]\frac{5}{7}[/tex] is a fraction

[tex]\frac{5}{7}[/tex] is a rational number

∵ 3.6820350285........ can not be written in the form of the fraction

   because we do not know its end (it is an approximated number)

∴ 3.6820350285........ is not a rational number

∵ -10 can be written as [tex]-\frac{10}{1}[/tex]

-10 is a rational number

0, 5/7, and -10 are RATIONAL numbers

Bob is hiking down a 12-mile country trail. He could hike at 3 mph for the first two hours and then go the rest of the way at 5 mph or he could just go the whole way at 4 mph. How long would each of these options take? Which option is the faster?
Answer:
The first option would take:
The second option would take:
The faster option is the:

Answers

Answer: The first option would take: 3.2 hr

The second option would take: 3 hr

The faster option is the: second

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

Speed = distance / time.

First option:

Walking  at 3mph for 2 hours will give 2*3 = 6 miles.

So for 6 miles travelling at 5 mph he will take 6/5 = 1.2 hours.

Total time = 3.2 hours.

Second option:

Walking for 12 miles at 4 mph will take him 12/4 = 3 hours.

The fastest option is the second one.

Information was collected on those who attended the opening of a new movie. The analysis found that 56 percent of the moviegoers were female, 26 percent were under age 25, and 17 percent were females under the age of 25. Find the probability that a moviegoer is either female or under age 25.

Answers

Answer:

65

Step-by-step explanation:

Please help It’s already due

Answers

Answer:

90

Step-by-step explanation:

the total interior angles of a triangle measure to 180 degrees.

55 + 35 = 90

180-90=90

Alex has to fill his 10 gallon fish tank with water. He only has a 1 pint bucket. How many times will he have to fill his bucket to fill the tank?

Answers

Answer:

80

Step-by-step explanation:

8 pints in a gallon so then you multiply 8 x 10 and get 80

80 pints fills 10 gallons

1. What is the value of 125 - 34 + 7 x 3?
a.) 294
c. 112
b. 252
d. 70

Answers

Answer:

c

Step-by-step explanation

7x3=21

125-34=91

91+21=112

the answer for the problem is 112.
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