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worty [1.4K]
2 years ago
13

Suppose S is a recursively defined set, defined by - the number 1 is in S - if n is in S, then so is 3n + 2 - if n is in S, then

so is 5n - 1 - if n is in S, then so is n + 7. Suppose you want to prove using structural induction that all members of S have a certain property. What do you have to prove in the base step?
Mathematics
1 answer:
Tatiana [17]2 years ago
8 0

Answer:

See answer below

Step-by-step explanation:

Using structural induction, we would have to prove that 1 and all the numbers derived from this fact, have the property.

That is to say, we would have to prove that

1, 3*1+2, 5*1-1 and 1+7 = {1, 4, 5, 8} have the property we want to prove S has.

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jeds market has a total of 26 employees. Each full time employee makes $275/ week, and each part-time employee makes $140/ week.
ollegr [7]

The number of full time employees is 17 and the number of part time employee is 9

Step-by-step explanation:

Step 1 :

Let f represent the number of full time employee and p represent the number of part time employee

Total number of employees = 26

Hence we have f + p = 26

Step 2 :

Wages of full time employee  = $275

Wages of part time employee = $140

Total wages paid by Jeds = $ 5935

Hence we have 275 f + 140 p = 5935

Step 3:

Solving the equations obtained in step 1 and step 2 we have

f + p = 26, Multiplying by 275 = > 275 f + 275 p = 7150

275 f + 140 p = 5935

Subtracting equation 2 from 1 we have

135 p = 1215 => p = 9

Substituting this in f + p = 26 gives, f + 9 = 26

So f = 17

Step 4 :

Answer :

The number of full time employees is 17 and the number of part time employee is 9

5 0
2 years ago
Max and his friend zeke are comparing their ages. they figure out that if they double maxs age from 3 years ago and add it to ze
chubhunter [2.5K]
The first step of solving this problem is to find your x, which is the unknown number. The unknown number is the age of Max. Once you find the x you can write out your equation.

The equation for this problem is:

2x+8=26

the first step is to subtract 8 from both sides so that all you have on the left side is 2x and your equation will look like ths:

2x=18

after subtracting the 8; divide everything by the coefficient of x which is 2, your result is:

x=9

Max is 9 years old.
7 0
3 years ago
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Johnny paid $19 for a pair of jeans. It was originally $33. What percent discount did he receive?
Ber [7]

Answer:

Approximately 42.42%

Step-by-step explanation:

If you subtract 42.42% from 33 it equals approx 19.

4 0
3 years ago
7a/3a+3-5/4a-4=3a/2a+2
jekas [21]
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4 0
3 years ago
Solve for u<br> 2- 5/6u is less then -3
statuscvo [17]

Answer:

2(u-5)-6u

2u-2•5

2u-10

2u-10-6u

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Step-by-step explanation:

8 0
3 years ago
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