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
Papessa [141]
3 years ago
10

Let D = E = {−2, −1, 0, 1, 2} Write negations for each of the following statements and determine which is true, the given statem

ent or its negation. a. ∀x ∈ D, ∃y ∈ E such that x + y = 1. b ∃x ∈ D such that ∀y ∈ E, x + y = y. c. ∀x ∈ D, ∃y ∈ E such that xy ≥ y. d. ∃x ∈ D such that ∀y ∈ E, x ≤ y.
Mathematics
1 answer:
vfiekz [6]3 years ago
5 0

Answer:

See explanation below.

Step-by-step explanation:

We use laws of quantifiers to write the negations. The negation of ∀w∃zP(w,z) is ∃w∀z¬P(w,z). The negation of ∃w∀zP(w,z) is ∀w∃z¬P(w,z), for a predicate P depending on w and z.  

a) Negation: ∃x ∈ D, such that ∀y ∈ E, x + y ≠ 1. In this case the negation is true, hence the original statement is false. Take x=-2∈D, and note that x+y≤0 for all y ∈ E. Therefore x+y is never 1.

b) Negation: ∀x ∈ D, ∃y ∈ E such that x + y ≠ y. Here, the original statement is true. Take x=0∈D, then x+y=0+y=y for all y∈E.

c) Negation: ∃x ∈ D, such that ∀y ∈ E, xy < y. In this case, the original statement is true. Given x∈D, take y=x∈E. Hence xy=x²≥x for all x∈D (this inequality is true for integers, and we can check it case by case in D).

d) Negation: ∀x ∈ D, ∃y ∈ E such that x > y. In this case, the original statement is true, take x=-2∈D. Then -2≤y for all y∈E.

You might be interested in
write the equation of the line that passes through the given points expressed in slope-intercept form. m=2/3, (-4,5)
solniwko [45]

Answer:

y = \frac{2}{3}x + \frac{23}{3}

Step-by-step explanation:

To write the equation of a line with a point and a slope, use the point-slope form of a linear equation. Substitute m = 2/3 and the point (-4,5) into the equation.

y - y_1 = m(x-x_1)\\y - 5 = \frac{2}{3}(x --4)\\y - 5 = \frac{2}{3}(x+4)

Convert to slope intercept form by using the distributive property.

y - 5 = \frac{2}{3}(x+4)\\y - 5 = \frac{2}{3}x +\frac{8}{3}\\y = \frac{2}{3}x + \frac{8}{3} + 5\\y = \frac{2}{3}x + \frac{23}{3}

7 0
2 years ago
Leslie ran 4 1/2 laps around the park in 3/4 hour. Kayla ran 3 1/2 laps around the same park in the same amount of time. How man
Arte-miy333 [17]
Leslie:
h= hours
3/4h=4 1/2 laps
divide both sides by 3/4 or .75
1 hour = 6 laps
Kayla:
3/4h= 3 1/2 laps
divide both sides by 3/4
1 hour = 4 2/3 laps
Leslie can do C
1_ 1/3 more laps in an hour than Kayla
5 0
3 years ago
What is the area of a square with a side length of 10cm?
natita [175]

Answer:

100cm

Step-by-step explanation:

10*10

4 0
2 years ago
Read 2 more answers
Where is 11/3 on a number line between 2 and 4
lions [1.4K]
Hiii! To work it out, you would have to do 11 ÷ 3. Which would equal 3.6 (Recurring).  If it's to one decimal place, it would be 4 if not, it would just be 3.6 ^^

Hope it helps!! Good luck~
7 0
3 years ago
Can someone answer this question please?
Effectus [21]

Answer:

5+9+-23

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • A rectangle has a perimeter of 64 inches. The length is 6 more than the width.
    6·1 answer
  • According to the diagram below, which similarity statements are true?<br>Check all that apply<br>​
    7·1 answer
  • The graph of y = -3x + 4 is:
    11·1 answer
  • ASAP help. <br>help help​
    8·2 answers
  • Find the LCM of 12, 15, 18
    15·1 answer
  • Solve for x, -3x + 8 &lt; 23
    13·2 answers
  • Whats the numerical number for 5
    7·1 answer
  • How do you play chess?
    5·1 answer
  • CAN SOMEONE PLEASE CHECK MY ANSWER!!
    7·1 answer
  • Replacing x with 0.75 in x 2 will give you an answer of 0.5625<br><br> TRUE OR FALSE.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!