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Recent questions tagged discrete-mathematics
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1
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
by
shreyo
73
views
discrete-mathematics
kenneth-rosen
lattice
0
votes
1
answer
2
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
by
lalitver10
107
views
group-theory
discrete-mathematics
test-series
zeal
1
vote
2
answers
3
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
by
rsansiya111
109
views
written-test
iit
discrete-mathematics
1
vote
1
answer
4
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 7
by
jugnu1337
106
views
discrete-mathematics
counting
test-series
0
votes
2
answers
5
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
by
prithatiti
98
views
propositional-logic
mathematical-logic
discrete-mathematics
0
votes
0
answers
6
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
by
kidussss
74
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
1
answer
7
Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
kidussss
asked
in
Combinatory
Jul 29
by
kidussss
56
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
1
answer
8
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
by
kidussss
59
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
1
answer
9
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
by
kidussss
99
views
mathematical-logic
discrete-mathematics
1
vote
1
answer
10
Made Easy Test Series
How to solve this question?
Abhrajyoti00
asked
in
Mathematical Logic
Jul 24
by
Abhrajyoti00
178
views
made-easy-test-series
combinatory
discrete-mathematics
0
votes
1
answer
11
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
by
Abhrajyoti00
91
views
graph-theory
bipartite-graph
discrete-mathematics
graph-planarity
1
vote
0
answers
12
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
by
jugnu1337
70
views
discrete-mathematics
probability
0
votes
0
answers
13
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 9
by
kidussss
148
views
discrete-mathematics
combinatory
recurrence-relation
2
votes
1
answer
14
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
by
khushitshah
121
views
combinatory
discrete-mathematics
counting
0
votes
0
answers
15
Introduction to Graph Theory Exercises
This is the problem snapshot
AngshukN
asked
in
Graph Theory
May 22
by
AngshukN
178
views
graph-theory
graph-connectivity
discrete-mathematics
0
votes
1
answer
16
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 19
by
AKS1236
92
views
combinatory
discrete-mathematics
0
votes
1
answer
17
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
by
ykrishnay
103
views
discrete-mathematics
engineering-mathematics
propositional-logic
kenneth-rosen
mathematical-logic
0
votes
0
answers
18
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
by
ykrishnay
101
views
discrete-mathematics
propositional-logic
engineering-mathematics
kenneth-rosen
mathematical-logic
0
votes
0
answers
19
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
by
ykrishnay
134
views
discrete-mathematics
propositional-logic
engineering-mathematics
kenneth-rosen
mathematical-logic
0
votes
0
answers
20
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
by
ykrishnay
77
views
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
0
votes
0
answers
21
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
by
ykrishnay
74
views
discrete-mathematics
propositional-logic
engineering-mathematics
kenneth-rosen
0
votes
0
answers
22
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
by
ykrishnay
62
views
discrete-mathematics
mathematical-logic
propositional-logic
engineering-mathematics
kenneth-rosen
1
vote
2
answers
23
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 18
by
jugnu1337
140
views
discrete-mathematics
recurrence-relation
0
votes
0
answers
24
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
by
ykrishnay
85
views
discrete-mathematics
mathematical-logic
propositional-logic
engineering-mathematics
kenneth-rosen
0
votes
0
answers
25
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
by
ykrishnay
55
views
discrete-mathematics
mathematical-logic
propositional-logic
engineering-mathematics
kenneth-rosen
1
vote
1
answer
26
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 24
by
Amlan Kumar Majumdar
113
views
discrete-mathematics
propositional-logic
0
votes
0
answers
27
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
by
ykrishnay
65
views
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
0
votes
1
answer
28
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
by
ykrishnay
145
views
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
0
votes
0
answers
29
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
by
ykrishnay
61
views
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
1
vote
1
answer
30
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
by
ykrishnay
104
views
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
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