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Recent questions tagged kenneth-rosen
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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.
22. For each of these statements find a domain for which thestatement is true and a domain for which the statement isfalse.a) Everyone speaks Hindi.b) There is someone ol...
ykrishnay
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ykrishnay
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Mar 18, 2022
Mathematical Logic
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kenneth-rosen
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kenneth h rosen chapter 1 excercise 1.3
Show that (p → q) ∧ (q → r) and (p → r) is a logically equivalent to each other
Show that (p → q) ∧ (q → r) and (p → r) is a logically equivalent to each other
ykrishnay
595
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ykrishnay
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Feb 22, 2022
Mathematical Logic
discrete-mathematics
mathematical-logic
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kenneth-rosen
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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.
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
1.4k
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ykrishnay
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Feb 21, 2022
Mathematical Logic
kenneth-rosen
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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
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 y...
ykrishnay
548
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ykrishnay
asked
Feb 21, 2022
Mathematical Logic
discrete-mathematics
mathematical-logic
propositional-logic
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kenneth-rosen
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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
Each of Exercises 16–28 asks you to show that two compoundpropositions are logically equivalent. To do this, either showthat both sides are true, or that both sides are...
ykrishnay
941
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ykrishnay
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Feb 21, 2022
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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
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. Supp...
ykrishnay
724
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ykrishnay
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Feb 16, 2022
Mathematical Logic
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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 ?
From where can i get full solution of Discrete Mathematics and Its Applications by Kenneth H. Rosen ?
kaleen bhaiya
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kaleen bhaiya
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Jan 23, 2022
Mathematical Logic
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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 $14.$
Solve the recurrence relation for the number of rounds in the tournament described in question $14.$
admin
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admin
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May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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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?
How many rounds are in the elimination tournament described in question $14$ when there are $32$ teams?
admin
526
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admin
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May 9, 2020
Combinatory
kenneth-rosen
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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.
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 pl...
admin
1.8k
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admin
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May 9, 2020
Combinatory
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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. $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
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
551
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admin
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May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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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 $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
Find $f (n)$ when $n = 3k,$ where $f$ satisfies the recurrence relation $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
admin
641
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admin
asked
May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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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.
Give a big-O estimate for the function $f$ in question $10$ if $f$ is an increasing function.
admin
370
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admin
asked
May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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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 $f (n) = f (n/2) + 1 \:\text{with}\: f (1) = 1.$
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
373
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admin
asked
May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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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 $f (5)$ $f (125)$ $f (3125)$
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
396
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admin
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May 9, 2020
Combinatory
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discrete-mathematics
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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 $f (2)$ $f (8)$ $f (64)$ $(1024)$
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)$$(1024)$
admin
725
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admin
asked
May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 8.3 Question 7 (Page No. 535)
Suppose that $f (n) = f (n/3) + 1$ when $n$ is a positive integer divisible by $3,$ and $f (1) = 1.$ Find $f (3)$ $f (27)$ $f (729)$
Suppose that $f (n) = f (n/3) + 1$ when $n$ is a positive integer divisible by $3,$ and $f (1) = 1.$ Find$f (3)$$f (27)$$f (729)$
admin
495
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admin
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May 9, 2020
Combinatory
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discrete-mathematics
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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?$
How many operations are needed to multiply two $32 \times 32$ matrices using the algorithm referred to in Example $5?$
admin
355
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admin
asked
May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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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.
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 multiplica...
admin
264
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admin
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May 9, 2020
Combinatory
kenneth-rosen
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50
Kenneth Rosen Edition 7 Exercise 8.3 Question 4 (Page No. 535)
Express the fast multiplication algorithm in pseudocode.
Express the fast multiplication algorithm in pseudocode.
admin
370
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admin
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May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 8.3 Question 3 (Page No. 535)
Multiply $(1110)_{2} \:\text{and}\: (1010)_{2}$ using the fast multiplication algorithm.
Multiply $(1110)_{2} \:\text{and}\: (1010)_{2}$ using the fast multiplication algorithm.
admin
334
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admin
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May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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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$?
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
356
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admin
asked
May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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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?
How many comparisons are needed for a binary search in a set of $64$ elements?
admin
432
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admin
asked
May 9, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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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}.$
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),$$ w...
admin
387
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admin
asked
May 6, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 8.2 Question 51 (Page No. 527)
Prove Theorem $4:$ Let $c_{1},c_{2},\dots,c_{k}$ be real numbers. Suppose that the characteristic equation $r^{k}-c_{1}r^{k-1}-\dots c_{k} = 0$ has $t$ distinct roots $r_{1},r_{2},\dots,r_{t}$ ... $\alpha_{i,j}$ are constants for $1 \leq i \leq t\:\text{and}\: 0 \leq j \leq m_{i} - 1.$
Prove Theorem $4:$ Let $c_{1},c_{2},\dots,c_{k}$ be real numbers. Suppose that the characteristic equation$$r^{k}-c_{1}r^{k-1}-\dots c_{k} = 0$$has $t$ distinct roots $r_...
admin
362
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admin
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May 6, 2020
Combinatory
kenneth-rosen
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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.]
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 sub...
admin
409
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admin
asked
May 6, 2020
Combinatory
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 $C_{n}.$
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 $n$ e...
admin
258
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admin
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May 6, 2020
Combinatory
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Kenneth Rosen Edition 7 Exercise 8.2 Question 49 (Page No. 527)
Use question $48$ to solve the recurrence relation $(n + 1)a_{n} = (n + 3)a_{n-1} + n, \:\text{for}\: n \geq 1, \:\text{with}\: a_{0} = 1$
Use question $48$ to solve the recurrence relation $(n + 1)a_{n} = (n + 3)a_{n-1} + n, \:\text{for}\: n \geq 1, \:\text{with}\: a_{0} = 1$
admin
229
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admin
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May 6, 2020
Combinatory
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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 $48-50$ ...
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} = ...
admin
412
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admin
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May 6, 2020
Combinatory
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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.
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...
admin
589
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admin
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May 6, 2020
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