Homework Answers
Add Answer to:
3. Let P(n) be the statement that a postage of n cents can be formed using...
4. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and...
4. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts of this exercise outline a strong induction proof that P (n) is true forn > 18. a) Show statements P(18), P(19), P (20), and P(21) are true, completing the basis step of the proof. b) What is the inductive hypothesis of the proof? c) What do you need to prove in the inductive step? d) Complete...
Prove the statement n cents of postage can be formed using just 4-cent and 11-cent stamps...
Prove the statement n cents of postage can be formed
using just 4-cent and 11-cent stamps using mathematical induction,
where n ≥ 30.
Click and drag the given steps (on the right) to the corresponding step names given on the left) to carry out the inductive steps of the proof, after the inductive hypothesis has already been assumed in (b). Step 1 Replace eight 4-cent stamps by three 11-cent stamps, and we have formed k+ 1 cents in postage (3....
Please show all the steps and explain. Prove that every amount of postage of 18 cents...
Please show all the steps and explain.
Prove that every amount of postage of 18 cents or more can be formed using just 4-cent and 7-cent stamps
Prove that every amount of postage of 18 cents or more can be formed using just 4-cent and 7-cent stamps
Instructions: Please show all of your work. Unsupported answers may receive no credit. 1. (20 pts)...
Instructions: Please show all of your work. Unsupported answers may receive no credit. 1. (20 pts) Use mathematical induction to show that for integers n 21, 2.21 +3.22 + ... + (n + 1)21 = n. 21+1 w 2. (20 pts) Let P(n) be statement that a postage of n cents can be formed using only 4-cent and 7-cent stamps. Using strong induction, prove P(n) is true for n 2 18.
Problem 1 148pts] (1) I 10pts! Let P(n) be the statement that l + 2 +...
Problem 1 148pts] (1) I 10pts! Let P(n) be the statement that l + 2 + + n n(n + 1) / 2 , for every positive integer n. Answer the following (as part of a proof by (weak) mathematical induction): 1. [2pts] Define the statement P(1) 2. [2pts] Show that P(1 is True, completing the basis step. 3. [4pts] Show that if P(k) is True then P(k+1 is also True for k1, completing the induction step. [2pts] Explain why...
Use strong induction to show that any amount of postage more than one cent can be formed using just two-cent and three-cent stamps. (please be detailed!)
Use strong induction to show that any amount of postage more than one cent can be formed using just two-cent and three-cent stamps. (please be detailed!)
Let S(n) be a statement parameterized by a positive integer n. Consider a proof that uses...
Let S(n) be a statement parameterized by a positive integer n. Consider a proof that uses strong induction to prove that for all n 4.S(n) is true. The base case proves that S(4), S(5), S(6), S(7), and S(8) are all true. Select the correct expressions to complete the statement of what is assumed and proven in the inductive step. Supposed that for k> (1?),s() is true for everyj in the range 4 through k. Then we will show that (22)...
Use mathematical induction to prove that the statement is true for every positive integer n. 1'3+...
Use mathematical induction to prove that the statement is true for every positive integer n. 1'3+ 24 +3'5 +...+() = (n (n+1)(2n+7))/6 a. Define the last term denoted by t) in left hand side equation. (5 pts) b. Define and prove basis step. 3 pts c. Define inductive hypothesis (2 pts) d. Show inductive proof for pik 1) (10 pts)
(3) Uee mathematical induction to prove that the statement Vne ZtXR<n) → (2n+/< 2")) is true....
(3) Uee mathematical induction to prove that the statement Vne ZtXR<n) → (2n+/< 2")) is true. (Suggestion : Let Ple) dernote the sentence "(2<n)-> (21+k< 20)". In carrying out the proof of the inductive step Van Zyl onafhan) consider the cases PQ)=P(2), P2)->P(3), and Pn>Plitr) for 173, Separately.)
3 For each positive integer n, define E(n) 2+4++2n (a) Give a recursive definition for E(n)....
3 For each positive integer n, define E(n) 2+4++2n (a) Give a recursive definition for E(n). (b) Let P(n) be the statement E(n) nn1)." Complete the steps below to give a proof by induction that P(n) holds for every neZ+ i. Verify P(1) is true. (This is the base step.) ii. Let k be some positive integer. We assume P(k) is true. What exactly are we assuming is true? (This is the inductive hypothesis.) iii. What is the statement P(k...
4. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts of this exercise outline a strong induction proof that P (n) is true forn > 18. a) Show statements P(18), P(19), P (20), and P(21) are true, completing the basis step of the proof. b) What is the inductive hypothesis of the proof? c) What do you need to prove in the inductive step? d) Complete...
Prove the statement n cents of postage can be formed
using just 4-cent and 11-cent stamps using mathematical induction,
where n ≥ 30.
Click and drag the given steps (on the right) to the corresponding step names given on the left) to carry out the inductive steps of the proof, after the inductive hypothesis has already been assumed in (b). Step 1 Replace eight 4-cent stamps by three 11-cent stamps, and we have formed k+ 1 cents in postage (3....
Please show all the steps and explain.
Prove that every amount of postage of 18 cents or more can be formed using just 4-cent and 7-cent stamps
Prove that every amount of postage of 18 cents or more can be formed using just 4-cent and 7-cent stamps
Instructions: Please show all of your work. Unsupported answers may receive no credit. 1. (20 pts) Use mathematical induction to show that for integers n 21, 2.21 +3.22 + ... + (n + 1)21 = n. 21+1 w 2. (20 pts) Let P(n) be statement that a postage of n cents can be formed using only 4-cent and 7-cent stamps. Using strong induction, prove P(n) is true for n 2 18.
Problem 1 148pts] (1) I 10pts! Let P(n) be the statement that l + 2 + + n n(n + 1) / 2 , for every positive integer n. Answer the following (as part of a proof by (weak) mathematical induction): 1. [2pts] Define the statement P(1) 2. [2pts] Show that P(1 is True, completing the basis step. 3. [4pts] Show that if P(k) is True then P(k+1 is also True for k1, completing the induction step. [2pts] Explain why...
Let S(n) be a statement parameterized by a positive integer n. Consider a proof that uses strong induction to prove that for all n 4.S(n) is true. The base case proves that S(4), S(5), S(6), S(7), and S(8) are all true. Select the correct expressions to complete the statement of what is assumed and proven in the inductive step. Supposed that for k> (1?),s() is true for everyj in the range 4 through k. Then we will show that (22)...
Use mathematical induction to prove that the statement is true for every positive integer n. 1'3+ 24 +3'5 +...+() = (n (n+1)(2n+7))/6 a. Define the last term denoted by t) in left hand side equation. (5 pts) b. Define and prove basis step. 3 pts c. Define inductive hypothesis (2 pts) d. Show inductive proof for pik 1) (10 pts)
(3) Uee mathematical induction to prove that the statement Vne ZtXR<n) → (2n+/< 2")) is true. (Suggestion : Let Ple) dernote the sentence "(2<n)-> (21+k< 20)". In carrying out the proof of the inductive step Van Zyl onafhan) consider the cases PQ)=P(2), P2)->P(3), and Pn>Plitr) for 173, Separately.)
3 For each positive integer n, define E(n) 2+4++2n (a) Give a recursive definition for E(n). (b) Let P(n) be the statement E(n) nn1)." Complete the steps below to give a proof by induction that P(n) holds for every neZ+ i. Verify P(1) is true. (This is the base step.) ii. Let k be some positive integer. We assume P(k) is true. What exactly are we assuming is true? (This is the inductive hypothesis.) iii. What is the statement P(k...
Most questions answered within 3 hours.
-
The denaturation of proteins can be described by the
equilibrium
F⇌U
where F and U represent...
asked 58 minutes ago -
Please answer what the maximum and minimum force is, and the
angle on the ion is...
asked 1 hour ago -
implement a program that reads a number of rows and a symbol.
The program will draw...
asked 1 hour ago -
Assume that when adults with smartphones are randomly selected,
45% use them in meetings or classes....
asked 1 hour ago -
Determine the number of formula units of
Na2SO4 and moles of oxygen contained in 8.11
moles...
asked 1 hour ago -
Explain in steps on the following code
What would be the output when executed
using System;...
asked 1 hour ago -
Given the information in the table, which of the following
statements is CORRECT?
Stock A
Stock...
asked 1 hour ago -
Write MARIE assembly language programs that do the following:
Write a program that inputs an integer...
asked 1 hour ago -
Explain an understanding of services and protocols.
Explain the job of DNS.
Explain the three email...
asked 1 hour ago -
(As soon as possible) Balance each of the following equations
according to the half-reaction method:
H2O2(aq)...
asked 2 hours ago -
A thin rod with a mass of 3.5kg and a length L=1.5 m is oriented
horizontally....
asked 2 hours ago -
Inheritance pattern in BRCA 1
Describe the inheritance pattern of BRCA 1 Is it recessive or...
asked 2 hours ago