Whether the number 123,456,789 is divisible by 2.

Question

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Answer 1

Question

Chapter 5.1, Problem 16E

(a)

To determine

Whether the number 123,456,789 is divisible by 2.

(b)

To determine

Whether the number 123,456,789 is divisible by 3.

(c)

To determine

Whether the number 123,456,789 is divisible by 4.

(d)

To determine

Whether the number 123,456,789 is divisible by 5.

(e)

To determine

Whether the number 123,456,789 is divisible by 6.

(f)

To determine

Whether the number 123,456,789 is divisible by 8.

(g)

To determine

Whether the number 123,456,789 is divisible by 9.

(h)

To determine

Whether the number 123,456,789 is divisible by 10.

(i)

To determine

Whether the number 123,456,789 is divisible by 12.

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In this exercise, we will investigate a technique to prove that a language is notregular. This tool is called the pumping lemma.The pumping lemma says that if M = (S, I, f, s0, F ) is a DFA with p states (i.e., p = |S|) and if the wordw is in L(M ) (the language generated by M ) and w has length greater than or equal to p, then w may bedivided into three pieces, w = xyz, satisfying the following conditions:1. For each i ∈ N, xy^i z ∈ L(M ).2. |y| > 0 (i.e., y contains at least one character).3. |xy| ≤ p (i.e., the string xy has at most p characters). Use the pumping lemma to show the following language is not regular (HINT: Use proof by contradictionto assume the language is regular and apply the pumping lemma to the language):L = {0^k1^k | k ∈ N}

A prefix of length ℓ of some word w are the first ℓ characters (in order) of w.1. Construct a context-free grammar for the language: L = {w ∈ {a, b}∗ | every prefix of w has at least as many a’s as b’s}2. Explain why every word generated by your context-free grammar (in Part 1) is contained in L. Then,prove via induction that every w ∈ L is produced by your context-free grammar.

Answer 2

Question

Chapter 5.1, Problem 16E

(a)

To determine

Whether the number 123,456,789 is divisible by 2.

(b)

To determine

Whether the number 123,456,789 is divisible by 3.

(c)

To determine

Whether the number 123,456,789 is divisible by 4.

(d)

To determine

Whether the number 123,456,789 is divisible by 5.

(e)

To determine

Whether the number 123,456,789 is divisible by 6.

(f)

To determine

Whether the number 123,456,789 is divisible by 8.

(g)

To determine

Whether the number 123,456,789 is divisible by 9.

(h)

To determine

Whether the number 123,456,789 is divisible by 10.

(i)

To determine

Whether the number 123,456,789 is divisible by 12.

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Answer 3

Question

Chapter 5.1, Problem 16E

(a)

To determine

Whether the number 123,456,789 is divisible by 2.

(b)

To determine

Whether the number 123,456,789 is divisible by 3.

(c)

To determine

Whether the number 123,456,789 is divisible by 4.

(d)

To determine

Whether the number 123,456,789 is divisible by 5.

(e)

To determine

Whether the number 123,456,789 is divisible by 6.

(f)

To determine

Whether the number 123,456,789 is divisible by 8.

(g)

To determine

Whether the number 123,456,789 is divisible by 9.

(h)

To determine

Whether the number 123,456,789 is divisible by 10.

(i)

To determine

Whether the number 123,456,789 is divisible by 12.

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Answer 4

Question

Chapter 5.1, Problem 16E

(a)

To determine

Whether the number 123,456,789 is divisible by 2.

(b)

To determine

Whether the number 123,456,789 is divisible by 3.

(c)

To determine

Whether the number 123,456,789 is divisible by 4.

(d)

To determine

Whether the number 123,456,789 is divisible by 5.

(e)

To determine

Whether the number 123,456,789 is divisible by 6.

(f)

To determine

Whether the number 123,456,789 is divisible by 8.

(g)

To determine

Whether the number 123,456,789 is divisible by 9.

(h)

To determine

Whether the number 123,456,789 is divisible by 10.

(i)

To determine

Whether the number 123,456,789 is divisible by 12.

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Answer 5

Chapter 5.1, Problem 16E

(a)

To determine

Whether the number 123,456,789 is divisible by 2.

(b)

To determine

Whether the number 123,456,789 is divisible by 3.

(c)

To determine

Whether the number 123,456,789 is divisible by 4.

(d)

To determine

Whether the number 123,456,789 is divisible by 5.

(e)

To determine

Whether the number 123,456,789 is divisible by 6.

(f)

To determine

Whether the number 123,456,789 is divisible by 8.

(g)

To determine

Whether the number 123,456,789 is divisible by 9.

(h)

To determine

Whether the number 123,456,789 is divisible by 10.

(i)

To determine

Whether the number 123,456,789 is divisible by 12.

Answer 6

Chapter 5.1, Problem 16E

(a)

To determine

Whether the number 123,456,789 is divisible by 2.

Answer 7

Chapter 5.1, Problem 16E

(a)

To determine

Whether the number 123,456,789 is divisible by 2.

Answer 8

(b)

To determine

Whether the number 123,456,789 is divisible by 3.

Answer 9

(b)

To determine

Whether the number 123,456,789 is divisible by 3.

Answer 10

(c)

To determine

Whether the number 123,456,789 is divisible by 4.

Answer 11

(c)

To determine

Whether the number 123,456,789 is divisible by 4.

Answer 12

(d)

To determine

Whether the number 123,456,789 is divisible by 5.

Answer 13

(d)

To determine

Whether the number 123,456,789 is divisible by 5.

Answer 14

(e)

To determine

Whether the number 123,456,789 is divisible by 6.

Answer 15

(e)

To determine

Whether the number 123,456,789 is divisible by 6.

Answer 16

(f)

To determine

Whether the number 123,456,789 is divisible by 8.

Answer 17

(f)

To determine

Whether the number 123,456,789 is divisible by 8.

Answer 18

(g)

To determine

Whether the number 123,456,789 is divisible by 9.

Answer 19

(g)

To determine

Whether the number 123,456,789 is divisible by 9.

Answer 20

(h)

To determine

Whether the number 123,456,789 is divisible by 10.

Answer 21

(h)

To determine

Whether the number 123,456,789 is divisible by 10.

Answer 22

(i)

To determine

Whether the number 123,456,789 is divisible by 12.

Answer 23

(i)

To determine

Whether the number 123,456,789 is divisible by 12.

Answer 24

Expert Solution & Answer

Answer 25

Expert Solution & Answer

Answer 26

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Answer 27

Ch. 5.1 - Decide whether each statement is true or false 1....Ch. 5.1 - Decide whether each statement is true or false. If...Ch. 5.1 - Decide whether each statement is true or false....Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Decide whether each statement is true or false. 7....Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Find all natural number factors of each...

Whether the number 123,456,789 is divisible by 2.

Solution Summary: The author explains that the number 123,456,789 is not divisible by 2.

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Whether the number 123,456,789 is divisible by 2.

Whether the number 123,456,789 is divisible by 3.

Whether the number 123,456,789 is divisible by 4.

Whether the number 123,456,789 is divisible by 5.

Whether the number 123,456,789 is divisible by 6.

Whether the number 123,456,789 is divisible by 8.

Whether the number 123,456,789 is divisible by 9.

Whether the number 123,456,789 is divisible by 10.

Whether the number 123,456,789 is divisible by 12.

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