You are a pickle fanatic and only order your pickles online from Papa Pete’s Pickle Emporium. All orders from Papa Pete’s must be in sets of either three or seven jars. For example, you could order 20 jars by doing 3 + 3 + 7 + 7 (this is two sets of three and two sets of seven). Use strong induction to prove that you can order any number n of jars where n is a natural number and n >= 12. Be sure to clearly show/state your base cases, inductive hypothesis, what you wish to prove using the IH, and inductive step.

Q: Use the principle of mathematical induction to prove the statement below. You should have an…

A: Given that a0=6, an=3an-1     for n≥1.To show: an=6.3n   for all integers n≥0.

Q: What is wrong with the "proof"? Claim: All cats have the same fur Proof: By induction on n, the…

A: Take k=2 and try to go from n=1 to n=2.

Q: Show that for all n> 14, n cents can be represented by some combination of 3-cent coins and 8-cent…

A:

Q: After a day of skiing a family of six washes all of their ski-wear including their gloves. The next…

A:

Q: Use strong induction to show that if you currun one me or two miles, and if you can always run two…

A:

Q: Prove by induction ? 뉴스금 i=

A:

Q: Many people are standing in line to purchase theater tickets. The first person in line is a woman…

A: Here given that a crowd of n people stand in line to purchase a movie ticket. Firstperson in the…

Q: How many permutation can we make if we have 12 elements and use 4 at a time?

A: Given data:   The total numbers of elements are n=12. The numbers of elements used at a time are…

Q: A certain three-cylinder combination lock has 80 numbers on it. To open it, you turn to a number on…

A:

Q: Prove by induction that for positive integers n, 4|(5¹ +34n+3).

A: We have to prove by induction that for positive integers n, 4|5n+34n+3.

Q: 9) Let a, = a-1 +12a__2,a, = 2, a, = 1.Use the strong induction to show that for all n20, a, = (-3)"…

A:

Q: his is from a pretty basic proofs class. Prove True or False: if a|(bc), then a|b and a|c . I've…

A: False

Q: A box contain 8 red and 6 green balls. In how many ways can 3 balls be drawn such that they are all…

A:

Q: For this Big Problem, we're going to investigate induction in different settings, and think about…

A: Please see the below picture for detailed solution.

Q: Part A Prove the following theorem using either regular or strong induction. Theorem: Suppose that n…

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Q: The local post office offers stamps worth 4 cents and 5 cents. Prove that we can make any postage…

A:

Q: Prove (m) = m! n! (m-n)! using mathematical induction.

A: It shows above that the formula holds for k+1. By the principle of mathematical induction, the…

Q: or an integer n>=3, an n-gon is an n-sided polygon. (example, a 3-gon is a triangle, 4-gon is a…

A: To prove: the sum of the interior anles of every polygon with n sides is n-2180° Now we shall take a…

Q: Induction. 1.3 + 6+9+...+3n= 3n(n+ 1) , for n 1.

A:

Q: "For all integers a, b and c, if a | b and b | c, then a | (5b – 3c)"

A: 4. Given the integers a, b and c. To prove: If a/b and b/c, then a/5b-3c.

Q: A machinist produces 22 items during a shift. Three of the 22 items are defective and the rest are…

A: Here Given there are total 22 items produced during shifts and  19 are non defective and identical…

Q: Lab a) Prove by induction that if you have two sequences of numbers, a = ao, , An and b = bo, ...,…

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Q: How would I state the Principle of Mathematical Induction for P(b), b∈ N with only math symbols (no…

A:

Q: 5) Let a, = 2a +5,a, =1, use induction to show that a = 6(2")-5 for all n20.

A: Given that an=2an-1+5 and a0=1. We have to show that an=62n-5 for all n≥0. We have to use the…

Q: 3n couples and their one child sit at a round table in such a way that their one child is between a…

A: It is given that there are 3n couples and their one child sit at a round table in such a way that…

Q: There is a terribly designed set of stairs. It is not possible for you to step from one step to the…

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Q: Suppose that there is a bag containing 6 marbles. How many ways can you draw 4 marbles from the bag…

A: The bag contains =6 marbles number of marbles drawn=4

Q: Fibonacci-

A: Let p(n) be the statement:P(n):Basic step: so, p(1) is true.Now assume that, p(n) is true [Strong…

Q: A department store wants to send codes for  $15  off a  $75  purchase to the subscribers of its…

A: The coupon code have three letters followed by one digit and followed by one  letter. i.e. we have…

Q: aly (3) 2.3-1=3" – 1 i=1

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.