The number of partitions of the set { 1 , 2 , 3 , ... , 100 } are there such that there are exactly three parts.

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Answer 1

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Chapter 3.16, Problem 16.16E

a.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that there are exactly three parts.

b.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that elements 1,2 and 3 are in different parts.

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Design a PDA recognizing each of the following languages and draw its state diagram. Note that the transition function must be in the format of “a, b →c", namely we can only push/pop one symbol into/from the stack one time upon one input symbol. You will receive 0 point if you push/pop multiple symbols into/from the stack one time upon one input symbol. (1) {w|wa"b", n is odd} = (2) {w|w=w², length of w is odd and Σ = {a,b} } (3) {w|w= = a²b²n, n ≥1 } (4) {w|w= =a^bn+mcm, n≥0, m ≥ 1 } (5) {w|w=a²b³n, n≥0} (6) {w|w= = a¹³, n ≥ 1, m≥ 1 and n‡m } Hint: two cases: n > m and n

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a. Find the value of A.b. Find pX(x) and py(y).c. Find pX|y(x|y) and py|X(y|x)d. Are x and y independent? Why or why not?

Answer 2

Question

Chapter 3.16, Problem 16.16E

a.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that there are exactly three parts.

b.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that elements 1,2 and 3 are in different parts.

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Answer 3

Question

Chapter 3.16, Problem 16.16E

a.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that there are exactly three parts.

b.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that elements 1,2 and 3 are in different parts.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 3.16, Problem 16.16E

a.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that there are exactly three parts.

b.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that elements 1,2 and 3 are in different parts.

Expert Solution & Answer

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Answer 5

Chapter 3.16, Problem 16.16E

a.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that there are exactly three parts.

b.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that elements 1,2 and 3 are in different parts.

Answer 6

Chapter 3.16, Problem 16.16E

a.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that there are exactly three parts.

Answer 7

Chapter 3.16, Problem 16.16E

a.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that there are exactly three parts.

Answer 8

b.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that elements 1,2 and 3 are in different parts.

Answer 9

b.

To determine

The number of partitions of the set {1,2,3,...,100} are there such that elements 1,2 and 3 are in different parts.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 3.14 - Write the following relations on the set 1,2,3,4,5...Ch. 3.14 - Prob. 14.2E Ch. 3.14 - Prob. 14.3E Ch. 3.14 - For each of the following relations on the set of...Ch. 3.14 - Prob. 14.5E Ch. 3.14 - Prob. 14.6E Ch. 3.14 - Prob. 14.7E Ch. 3.14 - Prob. 14.8E Ch. 3.14 - Prob. 14.9E Ch. 3.14 - Prob. 14.10E

The number of partitions of the set { 1 , 2 , 3 , ... , 100 } are there such that there are exactly three parts.

Solution Summary: The author explains that the number of partitions of the set left1,2,3,mathrm...,100right are exactly three parts.

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The number of partitions of the set {1,2,3,...,100} are there such that there are exactly three parts.

The number of partitions of the set {1,2,3,...,100} are there such that elements 1,2 and 3 are in different parts.

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