1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lara [203]
3 years ago
12

Express the negations of each of these statements so that all negation symbols immediately precede predicates. a) ∀x∃y∀zT(x, y,

z) b) ∀x∃yP(x, y) ∨ ∀x∃yQ(x, y) c) ∀x∃y(P(x, y) ∧ ∃zR(x, y, z)) d) ∀x∃y(P(x, y) → Q(x, y))
Mathematics
2 answers:
sasho [114]3 years ago
5 0

Answer:

a) ∃x∀y∃z~T(x, y, z)

b) ∃x∀y~P(x, y) ∧ ∃x∀y~Q(x, y)

c) ∃x∀y(~P(x, y) ∨ ∀z~R(x, y, z))

d) ∃x∀y(P(x, y) → ~Q(x, y))

Step-by-step explanation:

The negation of a is written as ~a.

Note the following properties that are going to be applied in the problems here :

~(P → Q) = P → ~Q

De Morgan's Laws

~(P ∨ Q) = ~P ∧ ~Q

~(P ∧ Q) = ~P ∨ ~Q

~∃xP = ∀xP

~∀xP = ∃xP

So back to the original problem.

a) ∀x∃y∀zT(x, y, z)

We have the negation as

~[∀x∃y∀zT(x, y, z)]

= ∃x~∃y∀zT(x, y, z)

= ∃x∀y∀~zT(x, y, z)

= ∃x∀y∃z~T(x, y, z)

b) ∀x∃yP(x, y) ∨ ∀x∃yQ(x, y)

Negation is:

~[∀x∃yP(x, y) ∨ ∀x∃yQ(x, y)]

= ~∀x∃yP(x, y) ∧ ~∀x∃yQ(x, y)

= ∃x~∃yP(x, y) ∧ ∃x~∃yQ(x, y)

= ∃x∀y~P(x, y) ∧ ∃x∀y~Q(x, y)

c) ∀x∃y(P(x, y) ∧ ∃zR(x, y, z))

Negation is:

~[∀x∃y(P(x, y) ∧ ∃zR(x, y, z))]

= ~∀x∃y(P(x, y) ∧ ∃zR(x, y, z))

= ∃x~∃y(P(x, y) ∧ ∃zR(x, y, z))

= ∃x∀y~(P(x, y) ∧ ∃zR(x, y, z))

= ∃x∀y(~P(x, y) ∨ ~∃zR(x, y, z))

= ∃x∀y(~P(x, y) ∨ ∀z~R(x, y, z))

d) ∀x∃y(P(x, y) → Q(x, y))

Negation is:

~[∀x∃y(P(x, y) → Q(x, y))]

= ~∀x∃y(P(x, y) → Q(x, y))

= ∃x~∃y(P(x, y) → Q(x, y))

= ∃x∀y~(P(x, y) → Q(x, y))

= ∃x∀y(P(x, y) → ~Q(x, y))

Gnesinka [82]3 years ago
3 0

Answer:

a) ∀x∃y ¬∀zT(x, y, z)

∀x∃y ∃z ¬T(x, y, z)

b) ∀x¬[∃y (P(x, y) ∨ Q(x, y))]

∀x∀y ¬ [P(x, y) ∨ Q(x, y)]

∀x∀y [¬P(x, y) ^ ¬Q(x, y)]

c) ∀x ¬∃y (P(x, y) ^ ∃zR(x, y, z))

∀x ∀y ¬(P(x, y) ^ ∃zR(x, y, z))

∀x ∀y (¬P(x, y) v ¬∃zR(x, y, z))

∀x ∀y (¬P(x, y) v ∀z¬R(x, y, z))

d) ∀x¬∃y (P(x, y) → Q(x, y))

∀x∀y ¬(P(x, y) → Q(x, y))

∀x∀y (¬P(x, y) ^ Q(x, y))

You might be interested in
1. A jeepney driver claims that his average monthly income is Php 3000.00 with a standard deviation of Php 300.00. A sample of 3
nydimaria [60]

Answer:

Kindly check explanation

Step-by-step explanation:

The hypothesis :

H0 : μ = 3000

H0 : μ ≠ 3000

The test statistic :

(xbar - μ) ÷ (s/√(n))

xbar = 3500

μ = 3000

σ = 300

n = 30

(3500 - 3000) ÷ (350/√(30))

Test statistic = 7.824

Df = 30 - 1 = 29

Tcritical at 0.01 = 2.462

Test statistic > critical value ; we reject H0 ; and concluded that there is significant evidence that

μ ≠ 3000

7 0
3 years ago
1+1=<br> Easy question :&gt;
Veseljchak [2.6K]

1+1= 2

Big brain >:3 Ty for the points tho ^^

3 0
3 years ago
Read 2 more answers
What is the axis of symmetry of a parabola if its x-intercepts are -3 and 5?
ollegr [7]

Answer:

The axis of symmetry will be at 1

Step-by-step explanation:

The middle of -3 and 5 will be the axis :)

-3, -2, -1, 0, 1, 2, 3, 4, 5

-2, -1, 0, 1, 2, 3, 4

-1, 0, 1, 2, 3

0, 1, 2

1

3 0
3 years ago
1.) What is the mode of the data ? Show work ( A.3, B.5, C.8, D.10 )
ArbitrLikvidat [17]
Hey there.

1.) The mode is the number that's most frequent in a given list.
In our list, we have 2, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 10.
Our most frequent number is 6; therefore, our mode is 6.

2.) The median is the number in the middle of a list organized from least to greatest.
2, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 10;
4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9;
4, 5, 5, 5, 6, 6, 6, 6, 7;
5, 5, 5, 6, 6, 6, 6;
5, 5, 6, 6, 6;
5, 6, 6;
6.
6 is our median.

I hope this helps, despite your answer choices not providing the correct answer.
6 0
3 years ago
In 2000, Greenville had a population of 63,205 people. Greenville’s population increased by 2500 people each year. In 2000, Spri
Llana [10]

Answer:

year 6.6025 if there is no typo in your question and numbers are right.

Step-by-step explanation:

G = 63205 + 2500x

S = 50000 + 4500x

since 9% of 50000 = 0.09(50000) = 4500

find when G = S

63205 + 2500x = 50000 + 4500x

subtract both sides by 2500x to move x terms to the right

63205 = 50000 + 2000x

subtract both sides by 50000 to move the number to the left, so we can get like terms on each side

13205 = 2000x

divide both sides by 2000

x = 6.6025

6 0
2 years ago
Other questions:
  • 44 is 55% of what number?
    6·2 answers
  • Michael has 14 video games that he no longer plays. Five of the video games do not work. If he wants to sell the working video g
    15·2 answers
  • If f(x) =(1/9 ) (9x), what is f(3)
    5·1 answer
  • Which set of statements about the angles is true?
    15·1 answer
  • Which equation has the steepest graph?
    5·1 answer
  • If k/-8 = -7 then what is k?
    12·1 answer
  • HELP !!!!! the graph below shows arianas pay as a painter how much does ariana charge per painting
    9·2 answers
  • Which is the net for this rectangular prism?
    10·1 answer
  • A polygon is shown:
    12·2 answers
  • Find the distance between the two points in simplest radical form. (-1,7) and (8,-5)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!