Recent questions tagged kenneth-rosen / GATE Overflow for GATE CSE

Show that if f is a function from S to T , where S and T are finite sets with |S| |T |, then there are elements s1 and s2 in S such that f (s1) = f (s2), or in other wor...

Pineapple

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Pineapple asked Mar 23, 2023

1 votes

0 answers

6

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.

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 t...

Pineapple

1.2k views

Pineapple asked Mar 3, 2023

1 votes

0 answers

7

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.

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 i...

pavan singh

921 views

pavan singh asked Feb 16, 2023

0 votes

1 answer

8

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.

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....

pavan singh

3.6k views

pavan singh asked Feb 13, 2023

0 votes

1 answer

9

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.

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 sys...

pavan singh

764 views

pavan singh asked Jan 26, 2023

0 votes

1 answer

10

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

When does s∗ = s, where s is a compound proposition?

pavan singh

212 views

pavan singh asked Jan 22, 2023

0 votes

1 answer

11

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

Use truth tables to verify the absorption laws.a) p ∨ (p ∧ q) ≡ p b) p ∧ (p ∨ q) ≡ p

pavan singh

610 views

pavan singh asked Jan 21, 2023

0 votes

1 answer

12

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.

Show that each conditional statement in Exercise 10 is a tautology without using truth tables.

pavan singh

366 views

pavan singh asked Jan 21, 2023

0 votes

1 answer

13

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.

Show that each conditional statement in Exercise 9 is a tautology without using truth tables.

pavan singh

402 views

pavan singh asked Jan 21, 2023

0 votes

0 answers

14

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

Show that each of these conditional statements is a tautology by using truth tables.a) [¬p ∧ (p ∨ q)] → qb) [(p → q) ∧ (q → r)] → (p → r)c) [p ∧ (p →...

pavan singh

528 views

pavan singh asked Jan 21, 2023

0 votes

2 answers

15

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?

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 Fr...

pavan singh

1.5k views

pavan singh asked Jan 12, 2023

1 votes

2 answers

16

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?

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 sig...

pavan singh

1.4k views

pavan singh asked Jan 9, 2023

1 votes

2 answers

17

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.

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“...

pavan singh

2.0k views

pavan singh asked Jan 9, 2023

0 votes

1 answer

18

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.

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 l...

benzini

741 views

benzini asked Nov 29, 2022

1 votes

2 answers

19

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

Find a compatible total order for the divisibility relationon the set {1, 2, 3, 6, 8, 12, 24, 36}.

shreyo

495 views

shreyo asked Sep 26, 2022

0 votes

1 answer

20

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.

can this topic “PRENEX NORMAL FORM(PNF) ” is necsesary for gate or just i skip this topic.

ykrishnay

296 views

ykrishnay asked Apr 20, 2022

0 votes

0 answers

21

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 ?

49. a) Show that ∀xP (x) ∧ ∃xQ(x) is logically equivalentto ∀x∃y (P (x) ∧ Q(y)), where all quantifiers havethe same nonempty domain.b) Show that ∀xP (x) ∨...

ykrishnay

371 views

ykrishnay asked Apr 20, 2022

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0 answers

22

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.)

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...

ykrishnay

535 views

ykrishnay asked Apr 20, 2022

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0 answers

23

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)

Find a counterexample, if possible, to these universallyquantified statements, where the domain for all variablesconsists of all integers.a) ∀x∃y(x = 1/y)b) ∀x∃y(...

ykrishnay

332 views

ykrishnay asked Apr 19, 2022

0 votes

0 answers

24

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.

Find a common domain for the variables x, y, and zfor which the statement ∀x∀y((x = y) → ∀z((z = x) ∨(z = y))) is true and another domain for which it is false....

ykrishnay

251 views

ykrishnay asked Apr 18, 2022

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0 answers

25

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

Let Q(x, y) be the statement “x + y = x − y.” If the do-main for both variables consists of all integers, what arethe truth values?g) ∃y∀xQ(x, y)Basically i don...

ykrishnay

197 views

ykrishnay asked Apr 18, 2022

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0 answers

26

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.

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-t...

ykrishnay

309 views

ykrishnay asked Apr 16, 2022

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0 answers

27

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.

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 er...

ykrishnay

185 views

ykrishnay asked Apr 16, 2022

0 votes

0 answers

28

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

Exercises 46–49 establish rules for null quantification thatwe can use when a quantified variable does not appear in partof a statement.46. Establish these logical equi...

ykrishnay

401 views

ykrishnay asked Mar 20, 2022

0 votes

1 answer

29

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?

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 quantifie...

ykrishnay

1.1k views

ykrishnay asked Mar 19, 2022

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0 answers

30

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.

Express each of these statements using quantifiers. Thenform the negation of the statement, so that no negationis to the left of a quantifier. Next, express the negation ...

ykrishnay

199 views

ykrishnay asked Mar 19, 2022

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