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Recent questions and answers in Discrete Mathematics
2
votes
2
answers
1
GO Classes 2023 | Weekly Quiz 3 | Question: 12
An island has two kinds of inhabitants, knights, who always tell the truth, and knaves, who always lie. You encounter two people $A$ and $B$. What are $A$ and $B$ if: $A$ says $B$ is a knight and $B$ says The two of us are opposite types ? $A$ is ... , $B$ is knight $B$ is knight, $B$ is knave. $A$ is knave, $B$ is knave. $A$ is knave, $B$ is knight
Udhay_Brahmi
answered
in
Mathematical Logic
5 hours
ago
by
Udhay_Brahmi
126
views
goclasses
goclasses_wq3
mathematical-logic
propositional-logic
2-marks
0
votes
1
answer
2
NPTEL Assignment
In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together.
Coding skill
answered
in
Combinatory
3 days
ago
by
Coding skill
92
views
0
votes
1
answer
3
maths igate test series
Which of the relations below can also be characterized as a function defined on the set I = { 1, 2, 3, 4, 5 } { (x, y) | x, y ∈ I, x < y } B{ (x, y) | x, y ∈ I, x = 1 } C{ (x, y) | x, y ∈ I, x! = y } None of these
Aditya_
answered
in
Set Theory & Algebra
3 days
ago
by
Aditya_
50
views
functions
0
votes
1
answer
4
Kenneth Rosen Edition 7 Exercise 6.5 Question 59 (Page No. 434)
How many ways are there to distribute five balls into three boxes if each box must have at least one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?
ankit-saha
answered
in
Combinatory
4 days
ago
by
ankit-saha
119
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
1
vote
1
answer
5
Kenneth Rosen Edition 7 Exercise 6.5 Question 58 (Page No. 434)
How many ways are there to distribute five balls into seven boxes if each box must have at most one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?
ankit-saha
answered
in
Combinatory
4 days
ago
by
ankit-saha
164
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
0
votes
1
answer
6
Kenneth Rosen Edition 7 Exercise 6.5 Question 57 (Page No. 434)
How many ways are there to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs?
ankit-saha
answered
in
Combinatory
4 days
ago
by
ankit-saha
102
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
1
vote
1
answer
7
Kenneth Rosen Edition 7 Exercise 6.5 Question 56 (Page No. 434)
How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD?
ankit-saha
answered
in
Combinatory
4 days
ago
by
ankit-saha
112
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
50
votes
5
answers
8
GATE CSE 2003 | Question: 31
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\implies\) P(y) for all $x, y \in S$ satisfying $x \leq y$ ... for all x \(\in\) S such that b ≤ x and x ≠ c P(x) = False for all x \(\in\) S such that a ≤ x and b ≤ x
[ Jiren ]
answered
in
Set Theory & Algebra
Aug 12
by
[ Jiren ]
8.1k
views
gatecse-2003
set-theory&algebra
partial-order
normal
propositional-logic
1
vote
1
answer
9
Kenneth Rosen Edition 7 Exercise 6.1 Question 41 (Page No. 397)
A palindrome is a string whose reversal is identical to the string. How many bit strings of length $n$ are palindromes?
ankit-saha
answered
in
Combinatory
Aug 11
by
ankit-saha
114
views
kenneth-rosen
discrete-mathematics
counting
descriptive
1
vote
1
answer
10
Kenneth Rosen Edition 7 Exercise 6.1 Question 40 (Page No. 397)
How many subsets of a set with $100$ elements have more than one element?
ankit-saha
answered
in
Combinatory
Aug 11
by
ankit-saha
71
views
kenneth-rosen
discrete-mathematics
counting
descriptive
55
votes
14
answers
11
GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
Himanshu555
answered
in
Combinatory
Aug 11
by
Himanshu555
10.5k
views
gatecse-2015-set3
combinatory
normal
numerical-answers
3
votes
2
answers
12
GO Classes Scholarship 2023 | Test | Question: 11
Let $\text{U}$ be a set and $\text{X, Y} \subseteq \text{U}$. Define operation twist by $ \operatorname{twist}\text{(X, Y)} =(\text{X} \cap \text{Y}) \cup(\overline{\text{X}} \cap \overline{\text{Y}}). $ Which of the following ... $\operatorname{twist}\text{(X, Y)}=\operatorname{twist}(\overline{\text{X}}, \overline{\text{Y}})$
[ Jiren ]
answered
in
Set Theory & Algebra
Aug 9
by
[ Jiren ]
118
views
goclasses-scholarship-test1
goclasses
set-theory&algebra
set-theory
multiple-selects
2-marks
2
votes
3
answers
13
GO Classes Scholarship 2023 | Test | Question: 2
Let $\text{S}$ be the set of all bit-strings of length $7 .$ We define a relation $\mathrm{R}$ on the set $\mathrm{S}$ by the rule that $x\mathrm{R}y$ iff $x$ and $y$ ... such that $\forall j \neq i, x_{j}=y_{j}$ and $x_{i} \neq y_{i}$. What is the cardinality of relation $\mathrm{R}$?
Godlike
answered
in
Set Theory & Algebra
Aug 9
by
Godlike
321
views
goclasses-scholarship-test1
numerical-answers
goclasses
set-theory&algebra
relations
2-marks
4
votes
2
answers
14
GO Classes Scholarship 2023 | Test | Question: 4
Consider a $3 \times 11$ rectangular grid as depicted in Figure $1,$ formed by $33$ tiles of area $1\text{m}^2.$ A staircase walk is a path in the grid which moves only right or up. How many staircase walks are there from $\text{A}$ to $\text{B}$ which start by going to the right two times?
[ Jiren ]
answered
in
Combinatory
Aug 8
by
[ Jiren ]
192
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
1-mark
53
votes
8
answers
15
GATE CSE 2013 | Question: 26
The line graph $L(G)$ of a simple graph $G$ is defined as follows: There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$. For any two edges $e$ and $e'$ in $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if $e$ ... of a planar graph is planar. (S) The line graph of a tree is a tree. $P$ only $P$ and $R$ only $R$ only $P, Q$ and $S$ only
Jyotish Ranjan
answered
in
Graph Theory
Aug 7
by
Jyotish Ranjan
14.2k
views
gatecse-2013
graph-theory
normal
graph-connectivity
4
votes
2
answers
16
GO Classes Scholarship 2023 | Test | Question: 9
Consider the following graph $\text{G:}$ Let $\text{M, C, I, S, B, E}$ be the Matching number, chromatic number, independence number, Clique number, Vertex cover number, and edge cover number, respectively of $\text{G}.$ What is $\text{M+C+I+S+B+E}?$
Kabir5454
answered
in
Graph Theory
Aug 7
by
Kabir5454
162
views
goclasses-scholarship-test1
numerical-answers
goclasses
graph-theory
graph-connectivity
vertex-cover
2-marks
3
votes
1
answer
17
GO Classes Scholarship 2023 | Test | Question: 1
A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$. Which of the following options is/are false? Every Total relation is ... total and transitive, then $\mathrm{S}$ is an equivalence relation. The number of total relations on a set of $5$ elements is $1024.$
GO Classes
answered
in
Set Theory & Algebra
Aug 7
by
GO Classes
393
views
goclasses-scholarship-test1
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
4
votes
1
answer
18
GO Classes Scholarship 2023 | Test | Question: 3
Let $\text{A, B}$ be two disjoint non-empty sets. Let $\text{M}$ be the universal set and $\text{A} \cup \text{B}$ is a proper subset of $\mathrm{M}$. For any set $\mathrm{S}$, let $\mathrm{S}^{\prime}$ be the set of those elements ...
GO Classes
answered
in
Set Theory & Algebra
Aug 7
by
GO Classes
186
views
goclasses-scholarship-test1
goclasses
set-theory&algebra
set-theory
multiple-selects
2-marks
2
votes
1
answer
19
GO Classes Scholarship 2023 | Test | Question: 5
Consider $5$ cards, each has a distinct value from the set $\{2,3,4,5,6\},$ so there are $5$ different values, and we put them face down on the table. There are $5$ players and each player is given a number from $2$ ... with the value that player has. If no player loses, then the dealer loses. How many ways are there so that the dealer loses?
GO Classes
answered
in
Combinatory
Aug 7
by
GO Classes
138
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
2-marks
4
votes
1
answer
20
GO Classes Scholarship 2023 | Test | Question: 6
Consider three boxes and $12$ balls of the same size. We have $3$ indistinguishable red balls and $9$ distinguishable blue balls. The first box can fit at most three balls, the second box can fit at most four balls and the third box can fit ... all the red balls go into the same box. What is the total number of ways to put all the balls in the boxes?
GO Classes
answered
in
Combinatory
Aug 7
by
GO Classes
146
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
2-marks
2
votes
1
answer
21
GO Classes Scholarship 2023 | Test | Question: 7
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ ... $x^{5}$ is $\mathrm{G}(x)?$
GO Classes
answered
in
Combinatory
Aug 7
by
GO Classes
126
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
generating-functions
2-marks
3
votes
1
answer
22
GO Classes Scholarship 2023 | Test | Question: 8
In a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$, two nodes $u$ and $v$ are strongly connected if and only if they are mutually reachable i.e. there is a path from u to $v$ and a path from $v$ to $u$. ... connected components $\dots?$ can not increase can not decrease by more than $1$ can not decrease by more than $2$ may remain unchanged
GO Classes
answered
in
Graph Theory
Aug 7
by
GO Classes
110
views
goclasses-scholarship-test1
goclasses
graph-theory
graph-connectivity
multiple-selects
1-mark
3
votes
1
answer
23
GO Classes Scholarship 2023 | Test | Question: 10
For which of the following does there exist a graph satisfying the specified conditions? A tree with six vertices and six edges. A tree with three or more vertices, two vertices of degree one, and all the other vertices with degree three or ... with $10$ vertices and $8$ edges. A disconnected graph with $12$ vertices and $11$ edges and no cycle.
GO Classes
answered
in
Graph Theory
Aug 7
by
GO Classes
114
views
goclasses-scholarship-test1
goclasses
graph-theory
graph-connectivity
multiple-selects
2-marks
4
votes
1
answer
24
GO Classes Scholarship 2023 | Test | Question: 12
How many non-isomorphic simple undirected graphs are there, each with four vertices and without a cycle?
GO Classes
answered
in
Graph Theory
Aug 7
by
GO Classes
111
views
goclasses-scholarship-test1
numerical-answers
goclasses
graph-theory
graph-isomorphism
2-marks
4
votes
1
answer
25
GO Classes Scholarship 2023 | Test | Question: 13
Let $\text{T}_{n}$ be the number of ways to arrange cars in a row with $n$ parking spaces if we can use sedans, SUVs, trucks to park such that a truck requires two spaces, whereas a sedan or SUV requires just one space each, and No two ... i.e. initial conditions are already given, hence no need to compute them)
GO Classes
answered
in
Combinatory
Aug 7
by
GO Classes
176
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
recurrence-relation
2-marks
1
vote
2
answers
26
GO Classes 2023 | Weekly Quiz 3 | Question: 20
The implies connective $\rightarrow$ is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications. Which of the following statements is/are TRUE? For any propositions $P$ and $Q,$ the following is ... $R,$ the following statement is always true: $(P \rightarrow Q) \vee (R \rightarrow Q)$.
P SHANMUKHA SHARMA
answered
in
Mathematical Logic
Aug 6
by
P SHANMUKHA SHARMA
144
views
goclasses
goclasses_wq3
mathematical-logic
propositional-logic
multiple-selects
2-marks
0
votes
1
answer
27
Self doubt : Set Theory
At a family group meeting of 30 women, 17 are descended from George, 16 are descended from John, and 5 are not descended from George or John. How many of the 30 women are descended from both George and John?
Aditya_
answered
in
Set Theory & Algebra
Aug 4
by
Aditya_
68
views
set-theory
62
votes
12
answers
28
GATE CSE 1994 | Question: 1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
Cs_Gate_22
answered
in
Graph Theory
Aug 4
by
Cs_Gate_22
26.4k
views
gate1994
graph-theory
combinatory
normal
isro2008
counting
54
votes
13
answers
29
GATE CSE 2014 Set 1 | Question: 49
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. The set of all possible $1-$pennants is ${(1)}$, the set of all possible ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10-$pennants is________
Argharupa Adhikary
answered
in
Combinatory
Jul 31
by
Argharupa Adhikary
7.0k
views
gatecse-2014-set1
combinatory
numerical-answers
normal
43
votes
7
answers
30
GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
Argharupa Adhikary
answered
in
Combinatory
Jul 31
by
Argharupa Adhikary
8.7k
views
gatecse-2007
combinatory
0
votes
1
answer
31
Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
Kabir5454
answered
in
Combinatory
Jul 29
by
Kabir5454
43
views
discrete-mathematics
mathematical-logic
calculus
set-theory
15
votes
5
answers
32
GATE CSE 2002 | Question: 3
Let $A$ be a set of $n(>0)$ elements. Let $N_r$ be the number of binary relations on $A$ and let $N_f$ be the number of functions from $A$ to $A$ Give the expression for $N_r,$ in terms of $n.$ Give the expression for $N_f,$ terms of $n.$ Which is larger for all possible $n,N_r$ or $N_f$
Genius
answered
in
Set Theory & Algebra
Jul 29
by
Genius
2.9k
views
gatecse-2002
set-theory&algebra
normal
descriptive
relations
0
votes
1
answer
33
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 $(A\cap B) = \varnothing .$
Kabir5454
answered
in
Combinatory
Jul 29
by
Kabir5454
38
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
0
answers
34
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
47
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
0
answers
35
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
53
views
mathematical-logic
discrete-mathematics
35
votes
8
answers
36
GATE CSE 2009 | Question: 22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators
Argharupa Adhikary
answered
in
Set Theory & Algebra
Jul 26
by
Argharupa Adhikary
6.2k
views
gatecse-2009
set-theory&algebra
normal
group-theory
1
vote
1
answer
37
Made Easy Test Series
How to solve this question?
Aditya_
answered
in
Mathematical Logic
Jul 25
by
Aditya_
145
views
made-easy-test-series
combinatory
discrete-mathematics
1
vote
3
answers
38
GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 11
Let $P,S,R$ be three statements(propositions). Let $S$ be a sufficient condition for $P$, Let $R$ is a necessary condition for $P$ then which of the following is/are true? $S$ is a sufficient condition ... is neither sufficient, nor a necessary condition for $R.$ $S$ is a sufficient and necessary condition for $R$.
Argharupa Adhikary
answered
in
Mathematical Logic
Jul 25
by
Argharupa Adhikary
181
views
goclasses_wq2
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
0
votes
1
answer
39
Cengage algebra jee advanced.
Coefficient of x^8 in ( (1-x^6)/(1-x) )^3.
Kabir5454
answered
in
Combinatory
Jul 24
by
Kabir5454
88
views
combinatory
0
votes
1
answer
40
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
63
views
graph-theory
bipartite-graph
discrete-mathematics
graph-planarity
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