Suppose that P(n) is a propositional function. Determine for which nonnegative integers n the statement P(n) must be true if a) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 2) is true. b) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 3) is true. c) P(0) and P(1) are true; for all nonnegative integers n, if P(n) and P(n 1) are true, then P(n 2) is true. d) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 2) and P(n 3) are true

Answers

Answer 1

Solution :

a). [tex]$P(0)$[/tex] is true

Then ,[tex]$P(0+2)=P(2)$[/tex] is true.

         [tex]$P(2+2)=P(4)$[/tex] is true

          [tex]$P(4+2)=P(6)$[/tex] is true.

Therefore, we see that [tex]$P(n)$[/tex] is true for all the even integers : [tex]$\{0, 2,4,6,...\}$[/tex]

b). [tex]$P(0)$[/tex] is true

Then ,[tex]$P(0+3)=P(3)$[/tex] is true.

         [tex]$P(3+3)=P(6)$[/tex] is true

          [tex]$P(6+3)=P(9)$[/tex] is true.

Therefore, we see that [tex]$P(n)$[/tex] is true for all the multiples of 3 : [tex]$\{0, 3,6,9,12,...\}$[/tex]

c). [tex]$P(0)$[/tex] and [tex]$P(1)$[/tex] is true, then [tex]$P(0+2)=P(2)$[/tex] is true

[tex]$P(1)$[/tex] and [tex]$P(2)$[/tex] is true, then [tex]$P(1+2)=P(3)$[/tex] is true.

[tex]$P(2)$[/tex] and [tex]$P(3)$[/tex] is true, then [tex]$P(2+2)=P(4)$[/tex] is true.

So, we observe that  [tex]$P(n)$[/tex] is true for all the non- negative integers : [tex]$\{0, 1,2,3,4,5,6,...\}$[/tex].

d). [tex]$P(0)$[/tex] is true,

   So, [tex]$P(0+2)$[/tex] and [tex]$P(0+3)$[/tex] is true or [tex]$P(2)$[/tex] and [tex]$P(3)$[/tex] is true.

   Now,   [tex]$P(2)$[/tex] is true.

Again, [tex]$P(2+2)$[/tex] and [tex]$P(2+3)$[/tex] is true or [tex]$P(4)$[/tex] and [tex]$P(5)$[/tex] is true.

   Now, [tex]$P(3)$[/tex] is true.

Again, [tex]$P(3+2)$[/tex] and [tex]$P(3+3)$[/tex] is true or [tex]$P(5)$[/tex] and [tex]$P(6)$[/tex] is true.

Thus,

[tex]$P(n)$[/tex] is true for all the non- negative integers except 1 : [tex]$\{0, 2,3,4,5,6,...\}$[/tex].


Related Questions

could someone pls help me with this math problem?

Answers

The person up top is right that should be correct

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

A population of 470 animals decreases at an annual rate of 12%.

a.f(x)=470(1.88)x

b.f(x)=470(0.12)x

c.f(x)=470(0.88)x

d.f(x)=470(1.12)x

Answers

Answer:

C. f(x) = 470(0.88)ˣ

Step-by-step explanation:

Initial number =  470Decrease rate = 12%   ⇒ 100% - 12% = 88%   ⇒ 0.88 times

Required equation:

f(x) = 470(0.88)ˣ

Correct choice is C

PLZ HELP RN ILL MARK YOU BRAINLIST IF ITS RIGHT PLZZZ IM DESPERATE

Answers

Answer:

w = -0.5

Step-by-step explanation:

Divide the entire equation by -6.8 to cancel it out and get your "w" variable alone.

w = -0.5

Answer:

-0.5

Step-by-step explanation:

divide 3.4/-6.8= -0.5

Consider the following pair of equations:
-X - y = -5
y = x + 1
If the two equations are graphed, at what point do the
lines representing the two equations intersect? (4 points)
O (-2,3)
O (3,-2)
O (3, 2)
(23)
HELP ASAP

Answers

Answer:

Yeah i don't get it i have the same problem

Answer:

It is not (−2,3).

Step-by-step explanation:

mii need halp
im givin brainliest dis time

Answers

Answer:

x = 35 , y = 72.5

Step-by-step explanation:

(a)

x and 35° are vertical angles and are congruent, then

x = 35

(b)

y. y and 35 lie on a straight line and sum to 180°, that is

y + y + 35 = 180

2y + 35 = 180 ( subtract 35 from both sides )

2y = 145 ( divide both sides by 2 )

y = 72.5

Answer:

y = 72.5 degrees

X = 35 degrees

Step-by-step explanation: A straight line is 180 degrees. The line with the two y degrees and the 35 degrees is a straight line, which is = 180 degrees. Because the y degrees are the same variable (y) they are equal degrees. All you need to do to find y is 180-35 =145. Divide that by 2 to find both y’s. 145 / 2 = 72.5. You can do the same for x, or realize that x and 35 are alternate interior angles, meaning they are the same measure: 35 degrees.

four ways on how save water​

Answers

Turn off the faucet if not in use
Take shorter showers
Water your plants only when it needs it
Don’t throw trash on the sea

Nadia's class took a math test. The median score on the test was 72% and the mean of the test scores was 72%.

What does this tell you about the data set?

The data shows causation.

The data is accurate.

The data is symmetrical.

Answers

Answer:

C, or "The data is symmetrically"

Step-by-step explanation:

This is because when having both the median and the mean the same, this means their is a perfectly symmetrical distribution of data. Making both the mean and median the same.

The shape of a patio is triangle without hight of 8 ft and base of 17 ft what is the cost of out door carpeting to cover the patio of the carpeting costs 6.50 per ft

Answers

Answer:

$442

Step-by-step explanation:

Given :

Height of patio, h = 8ft

Base of patio = 17 ft

Cost of carpeting = $6.50 per ft²

Area of triangular patio :

Area = 1/2 * base * height

Area = 0.5 * 17 * 8

Area of patio = 4 * 17

Area of patio = 68 ft²

Cost of carpeting :

Area of patio * contains st per ft²

68 * 6.50

= $442

3x 2+ 4x - 20
using a area model.

Answers

Answer:

3x2+4x-2o= 12 metros se for quadrado se não será diferente a resposta

Change 22 metres per second to a speed in kilometres per hour.
Show your working clearly.

Answers

Answer:

79.2 km/hour

Step-by-step explanation:

1 m/sec= 3.6 km/hour 22m/sec= ? so just multiply 22 m/sec by 3.6 km/hour then the answer will be :- 79.2 km/hour

The distance a train travels between 2 cities is 540 miles. The train travels at a speed of 80 miles per hour. Matt set up these rates to find the time it took the train to travel between the 2 cities.

Answers

Answer:

it takes 6 hours 40 minutes

Answer: 6.75 hours

Step-by-step explanation:

540%80=6.75

A company manufactures computers. Function N represents the number of components that a new employee can assemble per day. Function E represents the number of components that an experienced employee can assemble per day. In both functions, t represents the number of hours worked in one day.
N(t)=50t/t+4
E(t)= 70t/t+3

Which function describes the difference of the number of components assembled per day by the experienced and new employees?
A. D(t)= 10t(2t+13)/t+3
B. D(t)= 10t(2t+13)/ (t+4)(t+3)
C. D(t)= 10t(2t-13)/t+4
D. D(t)=10t(2t-13)/ (t+4)(t+3)

Answers

The difference of the number of components assembled per day by the experienced and new Employees is : D(t)= 10t(2t+13)/ (t+4)(t+3)

Here we perform subtraction :

D(t) = N(t) - E(t)

N(t) = 50t / (t+4)

E(t) = 70t / (t+3)

The difference :

D(t) = E(t) - N(t)

D(t) = [70t / (t+3)] - [50t / (t+4)]

The L.C.M of (t+3) and (t+4) is (t+3)(t+4)

[70t(t+4)] - [50t(t+3)] / (t+3)(t+4)

70t² + 280t - [50t² + 150t] / (t+3)(t+4)

[70t² + 280t - 50t² - 150t] / (t+3)(t+4)

20t² + 130t / (t+3)(t+4)

D(t) = 10t(2t + 13) / (t+3)(t+4)

The difference of the number of components assembled is : D(t)= 10t(2t+13)/ (t+4)(t+3)

Learn more : https://brainly.com/question/1166214

Answer:b

Step-by-step explanation:

plato

jack tripper has 5 girls in his home. He takes away 3 of them to do something that should not be named how many girls r left

Answers

Answer:

uh i think 2 i just want points

Step-by-step explanation:

Edward has $20,000 in a savings account that earns 13% interest per year. The interest is not compounded.How much interest will he earn in 1 year?

Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

$

Answers

Answer:

22,600

Step-by-step explanation:

22,600 will be your answer

Is negative 40 greater than 12

Answers

Answer:

No, 12 is greater than -40

Step-by-step explanation:

Answer: I think your question is: Is negative forty greater than positive 12. It is not greater. Even if it was negative 40 and negative 12 it still would not be greater. Hope this helps :)

Step-by-step explanation:

Can someone help me with Tuesday’s question??

Answers

Answer:

B

Step-by-step explanation:


If y=2x and 3x – 3y = 2, then x

Answers

Answer:

x = - 2/3

Step-by-step explanation:

2x = y

3x - 6x = 2

- 3x = 2

- 3x ÷ - 3 = 2 ÷ - 3

x = 2 ÷ - 3

x = - 2/3

The sales tax rate in Connecticut is 6.35%. Megan wants to buy a jacket with a $45.00 price tag. She has a gift card to the store she wants to use. What amount needs to be on the gift card for Megan to be able to buy the jacket using only the gift card?

Answers

Answer:

$47.86

Step-by-step explanation:

A tax is a compulsory amount levied by the government or an agency of the government on goods and services

Taxes increases the price of goods and services. Thus, the amount paid would increase by the tax rate

Amount that needs to be on the gift card = amount of tax + price of the jacket

Price of the jacket = $45

Amount of tax = percentage tax rate x price of the jacket

0.0635 x $45 = $2.86

$45 + $2.86 = $47.86

PLZ HELP ME WITH THIS, I'VE BEEN STUCK ON THIS FOR A WHILE.
You sell large and small pictures at a fair. You sell a total of 16 pictures and made a total of $350. If large pictures sell for $25 and small pictures sell for $20. How many of each did you sell?

Answers

Answer:

it is blink

Step-by-step explanation:

vgftr

HELP ME PLEASE!!,I WILL GIVE BRAINLIEST!!I PROMISE!!:)

Answers

D because the radical simplified is -sqrt of 6 / 3 and when you multiply D with the radical it gives you that answer.

A and B are independent events. Find P(A and B). P(A)=1/5, P(B)=3/7

Answers

Answer:

Step-by-step explanation:

In a family,the ages of children arranged from the youngest to the oldest are 2,6,y,14 and z.if the sequence of the ages is in an arithmetic progressions what is the ratio z:y​

Answers

Answer:

9/5

Step-by-step explanation:

The common difference = 6 - 2 = 4

The age after 6 is 6 + 4 = 10 = y

The age after 14 is 14 + 4 = 18 = z

z/ y = 18/10 = 9/5

24% of 40



I need it worked out pls thank uuu:)










Answers

Step-by-step explanation:

24% is the same as 6/25

[tex] \frac{6}{25} \times 40 \\ = \frac{48}{5} = 9.6[/tex]

Answer:

9.6

Step-by-step explanation:

24% of 40 = 0.24 × 40 = 9.6

Work out the value of x.

Answers

2x+3x=180
5x=180
x=180/5
x=36

A fourth grade teacher gives homework every night in both mathematics and language arts. The time to complete the mathematics homework has a mean of 10 minutes and a standard deviation of 3 minutes. The time to complete the language arts assignment has a mean of 12 minutes and a standard deviation of 4 minutes. The time to complete the mathematics and the time to complete the language arts homework has a correlation rho = -0.75. The variance of the time to complete the entire homework assignment is

Answers

Answer:

4

Step-by-step explanation:

Given that:

X = time taken to complete mathematics homework

Y= time taken to complete language homework

Standard deviation of X ; SD(X) = 3

Standard deviation of Y ; SD(Y) = 4

rho = - 0.375

rho = Cov(X, Y) / SD(X) * SD(Y)

-0.375 = COV(X, Y) / 3 * 4

COV(X, Y) = 12 * - 0.375

COV(X,Y) = - 4.5

Variance(X, Y) = V(X, Y)

V(X, Y) = V(X) + V(Y) + 2COV(X,Y)

V(X) =SD(X)² = 3² = 9

V(Y) = SD(Y)² = 4² = 16

V(X,Y) = 9 + 16 + 2(-4.5)

V(X, Y) = 16

SD(X, Y) = sqrt(V(X, Y)) = sqrt(16) = 4

Hence, standard deviation to complete entire homework, SD(X, Y) = 4

I'm sorry for asking so many math questions, I just need alot of help​

Answers

Answer:

20 = √3/2hypo

20×2=√3 hypo

40=√3 hypo

hypo =23

23² = 20² + x²

529= 400+x²

x²= 529-400

x²=129

x= 12.8

Simplify: 3x + 6y - (4x - 2y)

Answers

Answer:

-x + 8y

Step-by-step explanation:

plz help meh (ASAP) question below

Answers

Answer:

It's D I believe.

Step-by-step explanation:

I had this question before.. hopefully this helps

Natalie is playing the Integer Game and only shows you the four cards shown below. She tells you that the rest of her cards have the same values on them and match one of these four cards.

Answers

Missing part of question

(a) If all matching cards will increase her score by 18, what are the matching cards

(b) If all matching cards will decrease her score by 12, what are the matching cards

See attachment for cards

Answer:

(a) 9 card number 2 or 6 card number 3

(b) 6 card number -6

Step-by-step explanation:

Given

The number on the cards are: 2, 3, -6 and 4

Solving (a): An increment of 18

From the card numbers attached, there are 3 positive numbers and 1 negative number

If any of the card numbers is to increase her score, then the card number must be positive. So, we have: card numbers 2, 3 and 4 that fit in this category.

Next, for a card number to give an increment of 18; the card number must be a factor of 18.

So, we have:

[tex]\frac{18}{2} = 9[/tex]

[tex]\frac{18}{3} = 6[/tex]

[tex]\frac{18}{4} = 4.5[/tex]

Only 2 and 3 are factors of 18.

So, Natalie cards are: 9 card number 2 or 6 card number 3

Solving (b): A decrement of 12

If any of the card numbers is to decrease her score, then the card number must be negative. So, we have: card -6 that fit in this category.

Next, is to check if -12 is divisible by -6 (-12 means decrement of 12)

So, we have:

[tex]\frac{-12}{-6} = 2[/tex]

So, Natalie cards are: 6 card number -6

A circle with its dimensions, in centimeters (cm) is shown.
5 cm
What is the circumference, in centimeters, of the circle? Use 3.14 for. Round your answer to the nearest tenth

ANSWET FOR BRAINLIEST NOW

Answers

Step-by-step explanation:

add the radii to get the diameter then multipy by pi

10 (3.14) =31.4

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