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Recent questions tagged kennethrosen
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Rosen 7e Exercise8.5 Question15 page no558 InclusionExclusion
How many permutations of the 10 digits either begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions, or end with the 3 digits 123?
asked
May 24
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Combinatory
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aditi19
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discretemathematics
kennethrosen
inclusionexclusion
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Discrete Mathematics by Kenneth Rosen,section2.4,recursive functions
$C_{a}^{k}:\mathbb{N}^{k}\rightarrow \mathbb{N}$ I am studying discrete math from beginnings and came across this term in primitive recursive function.I don't know what $C_{a}^{k}$ means and does $\mathbb{N}$ means set of natural numbers?Someone please help me out.
asked
May 15
in
Set Theory & Algebra
by
souren
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37
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39
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discretemathematics
settheory&algebra
kennethrosen
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3
Rosen 7e Exercise 8.2 Questionno26 page no525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n1}$$12a_{n2}$+$8a_{n3}$+F(n) if F(n)=$n^2$ F(n)=$2^n$ F(n)=$n2^n$ F(n)=$(2)^n$ F(n)=$n^22^n$ F(n)=$n^3(2)^n$ F(n)=3
asked
May 14
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aditi19
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39
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kennethrosen
discretemathematics
#recurrencerelations
recurrence
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4
Rosen 7e Exercise8.2 Question no23 page no525 Recurrence Relation
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n1}$+$2^n$ in the book solution is given $a_n$=$2^{n+1}$ but I’m getting $a_n$=$3^{n+1}2^{n+1}$
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May 13
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Combinatory
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aditi19
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27
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kennethrosen
discretemathematics
#recurrencerelations
recurrence
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0
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5
Rosen 7e Exercise9.6 Question no27 page no631
What is the covering relation of the partial ordering {(A, B)  A ⊆ B} on the power set of S, where S = {a, b, c}? i'm getting R={(Ф, {a}), (Ф, {b}), (Ф, {c}), (Ф, {a, b}), (Ф, {b, c}), (Ф, {a, c}), (Ф, {a, b, c}), ({a}, {a, b}), ({a}, {a, c}), ({b}, ... b, c}), ({c}, {a, c}), ({c}, {b, c}), ({a, b}, {a, b, c}), ({a, c}, {a, b, c})({b, c}, {a, b, c})
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May 10
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Set Theory & Algebra
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aditi19
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56
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kennethrosen
discretemathematics
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settheory&algebra
settheory
sets
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6
Rosen 7e Recurrence Relation Exercise8.1 Question no25 page no511
How many bit sequences of length seven contain an even number of 0s? I'm trying to solve this using recurrence relation Is my approach correct? Let T(n) be the string having even number of 0s T(1)=1 {1} T(2)=2 {00, 11} T(3)=4 {001, ... add 0 to strings of length n1 having odd number of 0s T(n)=T(n1) Hence, we have T(n)=2T(n1)
asked
Apr 29
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Combinatory
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aditi19
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45
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kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
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1
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7
Rosen 7e Exercise8.1 Question no10 Page no511
Find a recurrence relation for the number of bit strings of length n that contain the string 01.
asked
Apr 28
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Combinatory
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aditi19
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45
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kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
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1
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8
Rosen 7e Exercise9.5 Question no9 page no615
Suppose that $A$ is a nonempty set, and $f$ is a function that has $A$ as its domain. Let $R$ be the relation on $A$ consisting of all ordered pairs $(x, y)$ such that $f (x)=f (y)$ $a)$ Show that $R$ is an equivalence relation on $A$ $b)$ What are the equivalence classes of $R?$
asked
Apr 23
in
Set Theory & Algebra
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aditi19
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43
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kennethrosen
discretemathematics
relations
equivalenceclasses
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9
Kenneth H Rosen 7th edition
Please see example 6. l am not getting the mathematical insight. Can anyone please tell how they are arriving at the answer.
asked
Apr 21
in
Combinatory
by
Psnjit
(
191
points)

50
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kennethrosen
discretemathematics
permutationandcombination
+2
votes
1
answer
10
Rosen 7e Exercise6.5 question 45.b page 433
How many ways can n books be placed on k distinguishable shelves if no two books are the same, and the positions of the books on the shelves matter?
asked
Apr 16
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Combinatory
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aditi19
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181
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kennethrosen
discretemathematics
permutationandcombination
0
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11
Kenneth Rosen Edition 7th Exercise 2.3 Question 74 (Page No. 155)
Prove or disprove each of these statements about the floor and ceiling functions. $\left \lfloor \left \lceil x \right \rceil \right \rfloor = \left \lceil x \right \rceil$ for all real numbers $x.$ ... $x$ and $y.$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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23
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kennethrosen
discretemathematics
settheory&algebra
0
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12
Kenneth Rosen Edition 7th Exercise 2.3 Question 73 (Page No. 155)
Prove or disprove each of these statements about the floor and ceiling functions. $\left \lceil \left \lfloor x \right \rfloor \right \rceil = \left \lfloor x \right \rfloor$ for all real number $x.$ ... $x.$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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31
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kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
13
Kenneth Rosen Edition 7th Exercise 2.3 Question 72 (Page No. 155)
Suppose that $f$ is a function from $A$ to $B$, where $A$ and $B$ are finite sets with $A=B$. Show that $f$ is onetoone if and only if it is onto.
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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35
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kennethrosen
discretemathematics
settheory&algebra
0
votes
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14
Kenneth Rosen Edition 7th Exercise 2.3 Question 71 (Page No. 155)
Let $S$ be a subset of a universal set $U$. The characteristic function $f_{s}$ of $S$ is the function from $U$ to the set $\left \{ 0,1 \right \}$ such that $f_{S}(x)=1$ if $x$ belongs to $S$ and $f_S(x)=0$ if $x$ does not belong to $S$. Let $A$ ... $f_{A \oplus B}(x) = f_{A}(x) + f_{B}(x) 2 f_{A}(x) f_{B}(x) $
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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18
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kennethrosen
discretemathematics
settheory&algebra
0
votes
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15
Kenneth Rosen Edition 7th Exercise 2.3 Question 70 (Page No. 155)
Suppose that $f$ is an invertible function from $Y$ to $Z$ and $g$ is an invertible function from $X$ to $Y$. Show that the inverse of the composition $fog$ is given by $(fog)^{1} = g^{1} o f^{1}.$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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24
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kennethrosen
discretemathematics
settheory&algebra
+1
vote
2
answers
16
Kenneth Rosen Edition 7th Exercise 2.3 Question 69 (Page No. 155)
Find the inverse function of $f(x) = x^3 +1.$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
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39
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
17
Kenneth Rosen Edition 7th Exercise 2.3 Question 68 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lceil 3x2 \right \rceil$ $f(x) =$ $\left \lceil 0.2x \right \rceil$ $f(x) =$ $\left \lfloor 1/x \right \rfloor$ $f(x) =$ $\left \lfloor x^2 \right \rfloor$ ... $f(x) =$ $\left \lfloor 2\left \lceil x/2 \right \rceil +1/2\right \rfloor$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

19
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
18
Kenneth Rosen Edition 7th Exercise 2.3 Question 67 (Page No. 155)
Draw graphs of each of these functions. $f(x) =$ $\left \lfloor x+1/2 \right \rfloor$ $f(x) =$ $\left \lfloor 2x+1 \right \rfloor$ $f(x) =$ $\left \lceil x/3 \right \rceil$ $f(x) =$ $\left \lceil 1/x \right \rceil$ ... $f(x) =$ $\left \lceil \left \lfloor x12 \right \rfloor + 1/2\right \rceil$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
points)

24
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
19
Kenneth Rosen Edition 7th Exercise 2.3 Question 66 (Page No. 155)
Draw the graph of the function $f(n) =$ $\left \lceil x \right \rceil +\left \lceil x/2 \right \rceil$ from $R$ to $R$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
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12
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
20
Kenneth Rosen Edition 7th Exercise 2.3 Question 65 (Page No. 155)
Draw the graph of the function $f(n) =$\left \lfloor x \right \rfloor +\left \lfloor x/2 \right \rfloor$ from $R$ to $R$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
points)

21
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
21
Kenneth Rosen Edition 7th Exercise 2.3 Question 64 (Page No. 155)
Draw the graph of the function $f(n) =$\left \lfloor x/2 \right \rfloor$ from $R$ to $R$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
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15
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
22
Kenneth Rosen Edition 7th Exercise 2.3 Question 63 (Page No. 155)
Draw the graph of the function $f(n) =$\left \lfloor 2x \right \rfloor$ from $R$ to $R$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
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22
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
23
Kenneth Rosen Edition 7th Exercise 2.3 Question 62 (Page No. 155)
Draw the graph of the function $f(n) = 1n^2$ from $Z$ to $Z$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
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5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
24
Kenneth Rosen Edition 7th Exercise 2.3 Question 61 (Page No. 155)
Data are transmitted over a particular Ethernet network in blocks of $1500$ octets (blocks of $8$ bits). How many blocks are required to transmit the following amounts of data over this Ethernet network? (Note that a byte is a synonym ... $1.544$ $\text{megabytes}$ of data $45.3$ $\text{megabytes of}$ data
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
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20
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
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25
Kenneth Rosen Edition 7th Exercise 2.3 Question 60 (Page No. 155)
How many ATM cells (described in Example 28) can be transmitted in $10$ seconds over a link operating at the following rates? $128$ kilobits per second ($1$ kilobit= $1000$ bits) $300$ kilobits per second $1$ megabit per second ($1$ megabit=$1,000,000$ bits)
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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8
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kennethrosen
discretemathematics
settheory&algebra
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26
Kenneth Rosen Edition 7th Exercise 2.3 Question 59 (Page No. 155)
How many bytes are required to encode $n$ bits of data where $n$ equals $7$ $17$ $1001$ $28800$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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5
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
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27
Kenneth Rosen Edition 7th Exercise 2.3 Question 58 (Page No. 154)
How many bytes are required to encode $n$ bits of data where $n$ equals $4$ $10$ $500$ $3000$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
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10
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kennethrosen
discretemathematics
settheory&algebra
0
votes
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28
Kenneth Rosen Edition 7th Exercise 2.3 Question 57 (Page No. 154)
Let $a$ and $b$ be real numbers with $a<b$. Use the floor and / or ceiling functions to express the number of integers $n$ that satisfy the inequality $a<n<b.$
asked
Apr 11
in
Set Theory & Algebra
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Pooja Khatri
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10.8k
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10
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kennethrosen
discretemathematics
settheory&algebra
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votes
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29
Kenneth Rosen Edition 7th Exercise 2.3 Question 56 (Page No. 154)
Let $a$ and $b$ be real numbers with $a<b$. Use the floor and / or ceiling functions to express the number of integers $n$ that satisfy the inequality $a≤n≤b$.
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
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17
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kennethrosen
discretemathematics
settheory&algebra
0
votes
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30
Kenneth Rosen Edition 7th Exercise 2.3 Question 55 (Page No. 154)
The function INT is found on some calculators, where INT$(x)$ = $\left \lfloor x \right \rfloor$ when $x$ nonnegative real number and INT$(x)$ = $\left \lceil x \right \rceil$ when x is a negative real number. Show that this INT function satisfies the identity INT$(x)$=$$ INT$(x)$
asked
Apr 11
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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