Recent questions tagged kenneth-rosen

Recent questions tagged kenneth-rosen

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kenneth h rosen chapter 1 section 1.5 PRENEX NORMAL FORM in excercise 1.5
can this topic “PRENEX NORMAL FORM(PNF) ” is necsesary for gate or just i skip this topic.

ykrishnay asked in Mathematical Logic Apr 20

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kenneth h rosen chapter 1 section section 1.5 nested quatnifiers excercise 49
49. a) Show that ∀xP (x) ∧ ∃xQ(x) is logically equivalent to ∀x∃y (P (x) ∧ Q(y)), where all quantifiers have the same nonempty domain. b) Show that ∀xP (x) ∨ ∃xQ(x) is equivalent to ∀x∃y (P (x) ∨ Q(y)), where all quantifiers have the same nonempty domain. please anybody tell how to prove this logical equivalency ?

ykrishnay asked in Mathematical Logic Apr 20

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kenneth h rosen chapter 1 section 1.5 nested quantifiers excercise 1.5 question 48

ykrishnay asked in Mathematical Logic Apr 20

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kenneth h rosen chapter 1 section nested quantifers excercise 1.5 question 40
Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all integers. a) ∀x∃y(x = 1/y) b) ∀x∃y(y^2 − x < 100)

ykrishnay asked in Mathematical Logic Apr 19

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kenneth h rosen chapter 1 section 1.5 nested quantifers question 34
Find a common domain for the variables x, y, and z for which the statement ∀x∀y((x = y) → ∀z((z = x) ∨ (z = y))) is true and another domain for which it is false.

ykrishnay asked in Mathematical Logic Apr 18

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kenneth h rosen chapter 1 section "Nested quantifers" excercise 1.5 question 26's g

ykrishnay asked in Mathematical Logic Apr 18

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kenneth h rosen chapter 1 section 1.5 excercise 1.5 question 18 e
Express each of these system specifications using predi- cates, quantifiers, and logical connectives, if necessary. e) No one knows the password of every user on the sys- tem except for the system administrator, who knows all passwords.

ykrishnay asked in Mathematical Logic Apr 16

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kenneth h rosen chapter 1 section 1.5 nested quantifiers excercise no 17, b
Express each of these system specifications using predi- cates, quantifiers, and logical connectives, if necessary. b)There is a process that continues to run during all error conditions only if the kernel is working correctly.

ykrishnay asked in Mathematical Logic Apr 16

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kenneth h rosen chapter 1 excercise 1.4 predicates and quantifiers question 46
Exercises 46-49 establish rules for null quantification that we can use when a quantified variable does not appear in part of a statement. 46. Establish these logical equivalences, where x does not occur as a free variable in A. Assume ... A ≡ ∃x(P (x) ∨ A) my doubt is wha is exactly A in in this logical expressions

ykrishnay asked in Mathematical Logic Mar 20

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kenneth h rosen chapter 1 excercise 1.4 predicates ad quantifiers question 59 symbolic logic

ykrishnay asked in Mathematical Logic Mar 19

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kenneth h rosen chapter 1 excercise 1.4 predicates ad quantifiers question 33
Express each of these statements using quantifiers. Then form the negation of the statement, so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the phrase It ... There is no dog that can talk. e) There is no one in this class who knows French and Russian.

ykrishnay asked in Mathematical Logic Mar 19

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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.

ykrishnay asked in Mathematical Logic Mar 18

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13

kenneth h rosen chapter 1 excercise 1.3
Show that (p → q) ∧ (q → r) and (p → r) is a logically equivalent to each other

ykrishnay asked in Mathematical Logic Feb 22

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14

kenneth h rosen chapter 1 excercise 1.3 question 56
Show that if p, q, and r are compound propositions such that p and q are logically equivalent and q and r are log- ically equivalent, then p and r are logically equivalent.

ykrishnay asked in Mathematical Logic Feb 21

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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

ykrishnay asked in Mathematical Logic Feb 21

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16

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 asked in Mathematical Logic Feb 21

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17

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 to a ... you say 'yes'? how this question arise and please explain the reason about this answer to above question thank you

ykrishnay asked in Mathematical Logic Feb 16

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18

Kenneth Rosen Edition 7th Exercise 8.3 Question 16 (Page No. 535)
Solve the recurrence relation for the number of rounds in the tournament described in question $14.$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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19

Kenneth Rosen Edition 7th 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?

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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20

Kenneth Rosen Edition 7th 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.

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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21

Kenneth Rosen Edition 7th 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. $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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22

Kenneth Rosen Edition 7th Exercise 8.3 Question 12 (Page No. 535)
Find $f (n)$ when $n = 3k,$ where $f$ satisfies the recurrence relation $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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23

Kenneth Rosen Edition 7th 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.

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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24

Kenneth Rosen Edition 7th Exercise 8.3 Question 10 (Page No. 535)
Find $f (n)$ when $n = 2^{k},$ where $f$ satisfies the recurrence relation $f (n) = f (n/2) + 1 \:\text{with}\: f (1) = 1.$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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25

Kenneth Rosen Edition 7th 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 $f (5)$ $f (125)$ $f (3125)$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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26

Kenneth Rosen Edition 7th 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 $f (2)$ $f (8)$ $f (64)$ $(1024)$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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27

Kenneth Rosen Edition 7th 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 $f (3)$ $f (27)$ $f (729)$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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28

Kenneth Rosen Edition 7th 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 $5?$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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29

Kenneth Rosen Edition 7th 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.

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

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30

Kenneth Rosen Edition 7th Exercise 8.3 Question 4 (Page No. 535)
Express the fast multiplication algorithm in pseudocode.

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

163 views

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