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Recent questions tagged kenneth-rosen

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Kenneth Rosen, exercise 6.1, Qs - 42 (d)
How many 4-element DNA sequences contain exactly three of the four bases A, T, C, and G? Solution given: There are four ways to choose which letter is to occur twice and three ways to decide which of the other letters to leave ... wrong. It would be of great help if you can show what combinations my approach is not including but the given solution includes.

Roshakaw asked in Combinatory Mar 3

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Discrete Maths by Kenneth Rosen, exercise 6.1, Qs - 12
How many bit strings are there of length six or less, not counting the empty string? Solution given:- We use the sum rule, adding the number of bit strings of each length up to 6. If we include the empty string, then we get 2^0 ... a binary string such as 000100 of length 3, and so on Please let me know if I am wrong somewhere in my approach.

Roshakaw asked in Combinatory Mar 2

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Kenneth Rosen Edition 7 Exercise 1.6 Question 11 (Page No. 79)
Show that the argument form with premises $p_1,p_2$,...,$p_n$ and conclusion q → r is valid if the argument form with premises $p_1,p_2,$...,$p_n$,q, and conclusion r is valid.

pavan singh asked in Mathematical Logic Feb 16

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Kenneth Rosen Edition 7 Exercise 1.6 Question 10 (Page No. 79)
For each of these sets of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises. a) If I play hockey, then I am sore the next day. ... or hallucinating. I am not dreaming. If I am hallucinating, I see elephants running down the road.

pavan singh asked in Mathematical Logic Feb 13

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Kenneth Rosen Edition 7 Exercise 1.3 Question 57 (Page No. 36)
The following sentence is taken from the specification of a telephone system: If the directory database is opened,then the monitor is put in a closed state, if the system is not in its initial ... statements. Find an equivalent, easier to understand specification that involves disjunctions and negations but not conditional statements.

pavan singh asked in Mathematical Logic Jan 26

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Kenneth Rosen Edition 7 Exercise 1.3 Question 36 (Page No. 35)
When does s∗ = s, where s is a compound proposition?

pavan singh asked in Mathematical Logic Jan 22

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Kenneth Rosen Edition 7 Exercise 1.3 Question 13 (Page No. 35)
Use truth tables to verify the absorption laws. a) p ∨ (p ∧ q) ≡ p b) p ∧ (p ∨ q) ≡ p

pavan singh asked in Mathematical Logic Jan 21

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Kenneth Rosen Edition 7 Exercise 1.3 Question 12 (Page No. 35)
Show that each conditional statement in Exercise 10 is a tautology without using truth tables.

pavan singh asked in Mathematical Logic Jan 21

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Kenneth Rosen Edition 7 Exercise 1.3 Question 11 (Page No. 35)
Show that each conditional statement in Exercise 9 is a tautology without using truth tables.

pavan singh asked in Mathematical Logic Jan 21

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Kenneth Rosen Edition 7 Exercise 1.3 Question 10 (Page No. 35)
Show that each of these conditional statements is a tautology by using truth tables. a) [¬p ∧ (p ∨ q)] → q b) [(p → q) ∧ (q → r)] → (p → r) c) [p ∧ (p → q)] → q d) [(p ∨ q) ∧ (p → r) ∧ (q → r)] → r

pavan singh asked in Mathematical Logic Jan 21

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Kenneth Rosen Edition 7 Exercise 1.2 Question 39 (Page No. 24)
Freedonia has fifty senators. Each senator is either honest or corrupt. Suppose you know that at least one of the Freedonian senators is honest and that, given any two Freedonian senators, at least one is corrupt. Based on ... you determine how many Freedonian senators are honest and how many are corrupt? If so, what is the answer?

pavan singh asked in Mathematical Logic Jan 12

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Kenneth Rosen Edition 7 Exercise 1.2 Question 37 (Page No. 24)
Suppose there are signs on the doors to two rooms. The sign on the first door reads In this room there is a lady, and in the other one there is a tiger ; and the sign on the second door reads In one of these rooms, ... tiger. Suppose that you know that one of these signs is true and the other is false. Behind which door is the lady?

pavan singh asked in Mathematical Logic Jan 9

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Kenneth Rosen Edition 7 Exercise 1.2 Question 36 (Page No. 24))
Four friends have been identified as suspects for an unauthorized access into a computer system. They have made statements to the investigating authorities. Alice said Carlos did it. John said I did not do it. Carlos said ... reasoning. b) If the authorities also know that exactly one is lying, who did it? Explain your reasoning.

pavan singh asked in Mathematical Logic Jan 9

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Discrete mathematics kenneth rosen
Determine whether the premises If I do not leave my home early or get stuck in a traffic jam, I will be late to my class and get scolded by my teacher , If I am late to my class, I will miss the attendance for the day , and ... today lead to the conclusion Therefore, I have left my home early today . Explain which rules of inference are used for each step.

benzini asked in Mathematical Logic Nov 30, 2022

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KENNITH ROSEN LATTICE
Find a compatible total order for the divisibility relation on the set {1, 2, 3, 6, 8, 12, 24, 36}.

shreyo asked in Set Theory & Algebra Sep 26, 2022

by shreyo

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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, 2022

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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, 2022

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kenneth h rosen chapter 1 section 1.5 nested quantifiers excercise 1.5 question 48
Show that ∀xP (x) ∨ ∀xQ(x) and ∀x∀y(P (x) ∨ Q(y)), where all quantifiers have the same nonempty domain, are logically equivalent. (The new variable y is used to combine the quantifications correctly.)

ykrishnay asked in Mathematical Logic Apr 20, 2022

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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, 2022

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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, 2022

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kenneth h rosen chapter 1 section "Nested quantifers" excercise 1.5 question 26's g
Let Q(x, y) be the statement “x + y = x − y.” If the do- main for both variables consists of all integers, what are the truth values? g) ∃y∀xQ(x, y) Basically i done all the subquestions (a,b,c,d,e,f,h,i) from this question but confused in g subquestion please give answer

ykrishnay asked in Mathematical Logic Apr 18, 2022

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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, 2022

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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, 2022

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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, 2022

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kenneth h rosen chapter 1 excercise 1.4 predicates ad quantifiers question 59 symbolic logic
Let P (x), Q(x), and R(x) be the statements x is a professor, x is ignorant, and x is vain, respectively. Express each of these statements using quantifiers; logical connectives; and P (x), Q(x), and ... c) follow from (a) and (b) what is the soution of d) cause i did not understand what the d) says?

ykrishnay asked in Mathematical Logic Mar 19, 2022

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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, 2022

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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, 2022

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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

ykrishnay asked in Mathematical Logic Feb 22, 2022

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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.

ykrishnay asked in Mathematical Logic Feb 21, 2022

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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, 2022

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