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Recent questions tagged kenneth-rosen
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31
kenneth h rosen excercise 1.4 predicates and quantifiers question 22
22. For each of these statements find a domain for which the statement is true and a domain for which the statement is false. a) Everyone speaks Hindi. b) There is someone older than 21 years. c) Every two people have the same first name. d) Someone knows more than two other people.
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Mar 18, 2022
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32
kenneth h rosen chapter 1 excercise 1.3
Show that (p → q) ∧ (q → r) and (p → r) is a logically equivalent to each other
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Feb 22, 2022
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33
Kenneth Rosen Edition 7 Excercise 1.3 Question 56 (Page No. 36)
Show that if p, q, and r are compound propositions such that p and q are logically equivalent and q and r are logically equivalent, then p and r are logically equivalent.
ykrishnay
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Feb 21, 2022
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ykrishnay
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kenneth-rosen
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0
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34
kenneth h rosen chapter 1 excercise 1.3 question 47
Show that p NAND q is logically equivalent to ¬(p ∧ q). how to prove this and i prove using truth table which is easy but how to prove using logical identities ? thank you
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Feb 21, 2022
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ykrishnay
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Kenneth h rosen chapter 1 excercise 1.3 question 16
Each of Exercises 16-28 asks you to show that two compound propositions are logically equivalent. To do this, either show that both sides are true, or that both sides are false, for exactly the same combinations ... combinations of truth values of the propositional variables in these expressions i didnt understand what statement says please tell
ykrishnay
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Mathematical Logic
Feb 21, 2022
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ykrishnay
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discrete-mathematics
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kenneth-rosen
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36
Kenneth h rosen chapter 1 excercise 1.2 question 15 on page 23
Each inhabitant of a remote village always tells the truth or always lies. A villager will give only a Yes or a No response to a question a tourist asks. Suppose you are a tourist visiting this area and come ... say 'yes'? how this question arise and please explain the reason about this answer to above question thank you
ykrishnay
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Mathematical Logic
Feb 16, 2022
by
ykrishnay
723
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discrete-mathematics
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kenneth-rosen
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37
Discrete Mathematics and Its Applications by Kenneth H. Rosen
From where can i get full solution of Discrete Mathematics and Its Applications by Kenneth H. Rosen ?
kaleen bhaiya
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Mathematical Logic
Jan 23, 2022
by
kaleen bhaiya
17.3k
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discrete-mathematics
kenneth-rosen
0
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1
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38
Kenneth Rosen Edition 7 Exercise 8.3 Question 16 (Page No. 535)
Solve the recurrence relation for the number of rounds in the tournament described in question $14.$
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Combinatory
May 9, 2020
by
admin
1.2k
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kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 8.3 Question 15 (Page No. 535)
How many rounds are in the elimination tournament described in question $14$ when there are $32$ teams?
admin
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May 9, 2020
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admin
524
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kenneth-rosen
discrete-mathematics
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40
Kenneth Rosen Edition 7 Exercise 8.3 Question 14 (Page No. 535)
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
admin
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Combinatory
May 9, 2020
by
admin
1.8k
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
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41
Kenneth Rosen Edition 7 Exercise 8.3 Question 13 (Page No. 535)
Give a big-O estimate for the function $f$ given below if $f$ is an increasing function. $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
admin
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Combinatory
May 9, 2020
by
admin
555
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
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Kenneth Rosen Edition 7 Exercise 8.3 Question 12 (Page No. 535)
Find $f (n)$ when $n = 3k,$ where $f$ satisfies the recurrence relation $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
admin
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in
Combinatory
May 9, 2020
by
admin
626
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
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Kenneth Rosen Edition 7 Exercise 8.3 Question 11 (Page No. 535)
Give a big-O estimate for the function $f$ in question $10$ if $f$ is an increasing function.
admin
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Combinatory
May 9, 2020
by
admin
355
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
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Kenneth Rosen Edition 7 Exercise 8.3 Question 10 (Page No. 535)
Find $f (n)$ when $n = 2^{k},$ where $f$ satisfies the recurrence relation $f (n) = f (n/2) + 1 \:\text{with}\: f (1) = 1.$
admin
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Combinatory
May 9, 2020
by
admin
364
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
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Kenneth Rosen Edition 7 Exercise 8.3 Question 9 (Page No. 535)
Suppose that $f (n) = f (n/5) + 3n^{2}$ when $n$ is a positive integer divisible by $5, \:\text{and}\: f (1) = 4.$ Find $f (5)$ $f (125)$ $f (3125)$
admin
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in
Combinatory
May 9, 2020
by
admin
393
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
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Kenneth Rosen Edition 7 Exercise 8.3 Question 8 (Page No. 535)
Suppose that $f (n) = 2f (n/2) + 3$ when $n$ is an even positive integer, and $f (1) = 5.$ Find $f (2)$ $f (8)$ $f (64)$ $(1024)$
admin
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Combinatory
May 9, 2020
by
admin
702
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kenneth-rosen
discrete-mathematics
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recurrence-relation
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47
Kenneth Rosen Edition 7 Exercise 8.3 Question 7 (Page No. 535)
Suppose that $f (n) = f (n/3) + 1$ when $n$ is a positive integer divisible by $3,$ and $f (1) = 1.$ Find $f (3)$ $f (27)$ $f (729)$
admin
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Combinatory
May 9, 2020
by
admin
476
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kenneth-rosen
discrete-mathematics
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recurrence-relation
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48
Kenneth Rosen Edition 7 Exercise 8.3 Question 6 (Page No. 535)
How many operations are needed to multiply two $32 \times 32$ matrices using the algorithm referred to in Example $5?$
admin
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Combinatory
May 9, 2020
by
admin
350
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kenneth-rosen
discrete-mathematics
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recurrence-relation
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Kenneth Rosen Edition 7 Exercise 8.3 Question 5 (Page No. 535)
Determine a value for the constant C in Example $4$ and use it to estimate the number of bit operations needed to multiply two $64$-bit integers using the fast multiplication algorithm.
admin
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Combinatory
May 9, 2020
by
admin
246
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
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50
Kenneth Rosen Edition 7 Exercise 8.3 Question 4 (Page No. 535)
Express the fast multiplication algorithm in pseudocode.
admin
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in
Combinatory
May 9, 2020
by
admin
359
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
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51
Kenneth Rosen Edition 7 Exercise 8.3 Question 3 (Page No. 535)
Multiply $(1110)_{2} \:\text{and}\: (1010)_{2}$ using the fast multiplication algorithm.
admin
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Combinatory
May 9, 2020
by
admin
334
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kenneth-rosen
discrete-mathematics
counting
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52
Kenneth Rosen Edition 7 Exercise 8.3 Question 2 (Page No. 535)
How many comparisons are needed to locate the maximum and minimum elements in a sequence with $128$ elements using the algorithm in Example $2$?
admin
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in
Combinatory
May 9, 2020
by
admin
348
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kenneth-rosen
discrete-mathematics
counting
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53
Kenneth Rosen Edition 7 Exercise 8.3 Question 1 (Page No. 535)
How many comparisons are needed for a binary search in a set of $64$ elements?
admin
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Combinatory
May 9, 2020
by
admin
424
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kenneth-rosen
discrete-mathematics
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recurrence-relation
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Kenneth Rosen Edition 7 Exercise 8.2 Question 52 (Page No. 527)
Prove Theorem $6:$Suppose that $\{a_{n}\}$ satisfies the liner nonhomogeneous recurrence relation $a_{n} = c_{1}a_{n-1} + c_{2}a_{n-2} + \dots + c_{k}a_{n-k} + F(n),$ where $c_{1}.c_{2},\dots,c_{k}$ ... solution of the form $n^{m}(p_{t}n^{t} + p_{t-1}n^{t-1} + \dots + p_{1}n + p_{0})s^{n}.$
admin
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in
Combinatory
May 6, 2020
by
admin
385
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kenneth-rosen
discrete-mathematics
counting
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Kenneth Rosen Edition 7 Exercise 8.2 Question 51 (Page No. 527)
Prove Theorem $4:$ Let $c_{1},c_{2},\dots,c_{k}$ be real numbers. Suppose that the characteristic equation $r^{k}-c_{1}r^{k-1}-\dots c_{k} = 0$ has $t$ distinct roots $r_{1},r_{2},\dots,r_{t}$ ... $\alpha_{i,j}$ are constants for $1 \leq i \leq t\:\text{and}\: 0 \leq j \leq m_{i} - 1.$
admin
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Combinatory
May 6, 2020
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admin
355
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kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 8.2 Question 53 (Page No. 527)
Solve the recurrence relation $T (n) = nT^{2}(n/2)$ with initial condition $T (1) = 6$ when $n = 2^{k}$ for some integer $k.$ [Hint: Let $n = 2^{k}$ and then make the substitution $a_{k} = \log T (2^{k})$ to obtain a linear nonhomogeneous recurrence relation.]
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Combinatory
May 6, 2020
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admin
393
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kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 8.2 Question 50 (Page No. 527)
It can be shown that Cn, the average number of comparisons made by the quick sort algorithm (described in preamble to question $50$ in exercise $5.4),$ when sorting $n$ ... $48$ to solve the recurrence relation in part $(A)$ to find an explicit formula for $C_{n}.$
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May 6, 2020
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admin
256
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kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 8.2 Question 49 (Page No. 527)
Use question $48$ to solve the recurrence relation $(n + 1)a_{n} = (n + 3)a_{n-1} + n, \:\text{for}\: n \geq 1, \:\text{with}\: a_{0} = 1$
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May 6, 2020
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admin
227
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kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 8.2 Question 48 (Page No. 526)
Some linear recurrence relations that do not have constant coefficients can be systematically solved. This is the case for recurrence relations of the form $f (n)a_{n} = g(n)a_{n-1} + h(n).$ Exercises $48-50$ ...
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May 6, 2020
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admin
403
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kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 8.2 Question 47 (Page No. 526)
A new employee at an exciting new software company starts with a salary of $\$50,000$ and is promised that at the end of each year her salary will be double her salary of the previous year, with an extra increment of $\ ... year of employment. Solve this recurrence relation to find her salary for her $n^{\text{th}}$ year of employment.
admin
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May 6, 2020
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admin
571
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