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121

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

476 views

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1 answer

122

Gate At Zeal
Question → If (G,*) is a group of order 960 and there exist a in G such that a^m=e for some integer m<=960 where e is identity element of G then total number of possible value of m is___________ Answer==28

lalitver10 asked in Set Theory & Algebra Sep 17, 2022

477 views

1 vote

2 answers

123

PhD Admissions Written Test (Basic)
Let x1, x2, ...x8 be 8 propositional variables. Let · represent AND connective ⊕ represent the Exclusive-or connective. The number of satisfying assignments of the formula x1 ⊕ x2 ⊕ ...x8 is _________________ The number of satisfying assignments of the formula (x1·x2) ⊕ (x3·x4)... ⊕ (x7·x8) is __________________

rsansiya111 asked in Mathematical Logic Sep 11, 2022

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1 vote

1 answer

124

igate test series
Selection of how many integers from the first ten positive integers (1, 2, ...) guarantees that there must be a pair of these integers with a sum equal to 11 ?

jugnu1337 asked in Combinatory Sep 6, 2022

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3 answers

125

Predicate Translation
S(x): x is a Student P(x): x is a Professor A(x, y): x has asked a question to y Domain not given, so we have to think about default domain Q1) Translate There is a student who has asked every professor a question Q2) Translate ... a professor who has been asked a question by every student Q4) Translate There is a student who has been asked a question by every professor

prithatiti asked in Mathematical Logic Sep 6, 2022

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0 answers

126

Mathematics for Natural Science
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$

kidussss asked in Combinatory Jul 29, 2022

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1 answer

127

Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$

kidussss asked in Combinatory Jul 29, 2022

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1 answer

128

Mathematics for Natural Science
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$

kidussss asked in Combinatory Jul 29, 2022

240 views

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1 answer

129

Mathematics for Natural Science
Suppose $x, y, z > 1$ are integers, let: $p(x,y)$ : $x$ is a factor of $y$ $q(x,y,z)$ : $z$ = $\text{GCD}(x,y)$ $r(x)$ : $x$ is prime. Check if the following argument is valid or not. $(\forall x \exists y)p(x,y) \implies r(x)$ ... $(\exists x)(\forall y)(p(x,y) \lor r(x))$ $\therefore (\forall y)(\exists z)(\exists x)q(x,y,z)$

kidussss asked in Mathematical Logic Jul 29, 2022

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1 vote

1 answer

130

Made Easy Test Series
How to solve this question?

Abhrajyoti00 asked in Mathematical Logic Jul 24, 2022

by Abhrajyoti00

440 views

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1 answer

131

Self Doubt - Planarity of Complete Bipartite Graph
How to determine for which m, n the complete bipartite graph $Km,n$ is planar? I am getting two answers from two sources:- A complete bipartite graph $Kmn$ is planar if and only if m<3 or n>3. Source: https://www.javatpoint.com/ ... m ≤ 2 or n ≤ 2. Source: http://www.matthewkahle.org/download/file/fid/573 Need a proper proof of the solution.

Abhrajyoti00 asked in Graph Theory Jul 21, 2022

by Abhrajyoti00

1.1k views

1 vote

0 answers

132

maths
A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card ?

jugnu1337 asked in Probability Jul 19, 2022

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0 answers

133

Discrete Mathematics and Combinatorics
Solve the recurrence relation $a^{2}n-5a^{2}_{n-1}+4a^{2} _{n-2}=0$, if $a_{0}=4, a_{1}=13, n>1$

kidussss asked in Combinatory Jul 8, 2022

476 views

2 votes

1 answer

134

no of solutions to the following inequality 12 <= w + x + y + z <= 14
No. of solutions to the following inequality 12 <= w + x + y + z <= 14 where w,x,y,z>=0

khushitshah asked in Combinatory Jun 8, 2022

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0 answers

135

Introduction to Graph Theory Exercises
This is the problem snapshot

AngshukN asked in Graph Theory May 22, 2022

397 views

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1 answer

136

A question paper is divided into two parts A and B and each part contains 5 questions. In how many ways a student can answer the question paper, if he has to solve total 6 questions including atleast 2 from each section.

AKS1236 asked in Combinatory May 18, 2022

762 views

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1 answer

137

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

287 views

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0 answers

138

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

363 views

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0 answers

139

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

528 views

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0 answers

140

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

317 views

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0 answers

141

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

236 views

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0 answers

142

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

192 views

1 vote

2 answers

143

recurrence relation
T(K)=5T(K-1)-4T(K-2) with initial condition T(0)=2 and T(1)=3 determine T(10). using recursion i got answer,but can anyone explain above method.

jugnu1337 asked in Set Theory & Algebra Apr 17, 2022

451 views

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0 answers

144

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

294 views

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0 answers

145

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

180 views

1 vote

1 answer

146

Doubt in By Case Method to check Tautology
The Truth Value of a compound proposition (if there two pv p,q) is depend on both pv...Then while checking tautology in by case method why we check only one pv’s case like p = true p =false..why we dont check q also?

Amlan Kumar Majumdar asked in Mathematical Logic Mar 23, 2022

by Amlan Kumar Majumdar

282 views

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0 answers

147

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

391 views

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1 answer

148

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

1.1k views

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0 answers

149

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

183 views

1 vote

1 answer

150

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

1.5k views

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Recent questions tagged discrete-mathematics