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Most viewed questions in Discrete Mathematics
88
votes
5
answers
31
GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
go_editor
asked
in
Mathematical Logic
Feb 13, 2015
by
go_editor
20.9k
views
gatecse-2015-set2
mathematical-logic
normal
first-order-logic
40
votes
6
answers
32
GATE CSE 2019 | Question: 38
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
Arjun
asked
in
Graph Theory
Feb 7, 2019
by
Arjun
20.4k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
2-marks
66
votes
10
answers
33
GATE CSE 2019 | Question: 35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... of all integers Which of the above sets satisfy $\varphi$? $S_1$ and $S_2$ $S_1$ and $S_3$ $S_2$ and $S_3$ $S_1, S_2$ and $S_3$
Arjun
asked
in
Mathematical Logic
Feb 7, 2019
by
Arjun
19.9k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
mathematical-logic
first-order-logic
2-marks
100
votes
11
answers
34
GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
Akash Kanase
asked
in
Mathematical Logic
Feb 12, 2016
by
Akash Kanase
19.7k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
60
votes
5
answers
35
GATE CSE 2007 | Question: 21
How many different non-isomorphic Abelian groups of order $4$ are there? $2$ $3$ $4$ $5$
Kathleen
asked
in
Set Theory & Algebra
Sep 21, 2014
by
Kathleen
19.5k
views
gatecse-2007
group-theory
normal
51
votes
15
answers
36
GATE CSE 2015 Set 2 | Question: 40
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
go_editor
asked
in
Set Theory & Algebra
Feb 12, 2015
by
go_editor
19.3k
views
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
59
votes
8
answers
37
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 ... 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
Arjun
asked
in
Graph Theory
Sep 24, 2014
by
Arjun
19.0k
views
gatecse-2013
graph-theory
normal
graph-connectivity
40
votes
7
answers
38
GATE CSE 2010 | Question: 28
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph? $7, 6, 5, 4, 4, 3, 2, 1$ $6, 6, 6, 6, 3, 3, 2, 2$ $7, 6, 6, 4, 4, 3, 2, 2$ $8, 7, 7, 6, 4, 2, 1, 1$ I and II III and IV IV only II and IV
gatecse
asked
in
Graph Theory
Sep 21, 2014
by
gatecse
18.4k
views
gatecse-2010
graph-theory
degree-of-graph
57
votes
11
answers
39
GATE CSE 2014 Set 3 | Question: 51
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $n-k$ $n-k+1$
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
18.3k
views
gatecse-2014-set3
graph-theory
graph-connectivity
normal
19
votes
18
answers
40
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
Arjun
asked
in
Combinatory
Feb 7, 2019
by
Arjun
18.1k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
0
votes
3
answers
41
NIELIT 2017 July Scientist B (IT) - Section B: 2
Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? In adjacency list representation, space is saved for sparse graphs. Deleting a vertex in adjacency list ... Adding a vertex in adjacency list representation is easier than adjacency matrix representation. All of the option.
admin
asked
in
Graph Theory
Mar 30, 2020
by
admin
17.7k
views
nielit2017july-scientistb-it
discrete-mathematics
graph-theory
44
votes
10
answers
42
GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
Akash Kanase
asked
in
Combinatory
Feb 12, 2016
by
Akash Kanase
17.7k
views
gatecse-2016-set2
modular-arithmetic
normal
numerical-answers
92
votes
12
answers
43
GATE CSE 2015 Set 3 | Question: 24
In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type ... person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail
go_editor
asked
in
Mathematical Logic
Feb 14, 2015
by
go_editor
17.7k
views
gatecse-2015-set3
mathematical-logic
difficult
logical-reasoning
89
votes
6
answers
44
GATE CSE 2006 | Question: 72
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The maximum degree of a vertex in $G$ is: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$
go_editor
asked
in
Graph Theory
Apr 24, 2016
by
go_editor
17.7k
views
gatecse-2006
graph-theory
normal
degree-of-graph
58
votes
9
answers
45
GATE CSE 2017 Set 2 | Question: 47
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
Arjun
asked
in
Combinatory
Feb 14, 2017
by
Arjun
17.6k
views
gatecse-2017-set2
combinatory
generating-functions
numerical-answers
normal
39
votes
8
answers
46
GATE CSE 2002 | Question: 1.25, ISRO2008-30, ISRO2016-6
The maximum number of edges in a $n$-node undirected graph without self loops is $n^2$ $\frac{n(n-1)}{2}$ $n-1$ $\frac{(n+1)(n)}{2}$
Kathleen
asked
in
Graph Theory
Sep 15, 2014
by
Kathleen
17.5k
views
gatecse-2002
graph-theory
easy
isro2008
isro2016
graph-connectivity
42
votes
6
answers
47
GATE CSE 2014 Set 2 | Question: 51
A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
17.4k
views
gatecse-2014-set2
graph-theory
numerical-answers
normal
graph-isomorphism
non-gate
44
votes
9
answers
48
GATE CSE 2017 Set 2 | Question: 23
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
Madhav
asked
in
Graph Theory
Feb 14, 2017
by
Madhav
17.3k
views
gatecse-2017-set2
graph-theory
numerical-answers
degree-of-graph
0
votes
2
answers
49
Discrete Mathematics and Its Applications by Kenneth H. Rosen
From where can i get full solution of Discrete Mathematics and Its Applications by Kenneth H. Rosen ?
kaleen bhaiya
asked
in
Mathematical Logic
Jan 23, 2022
by
kaleen bhaiya
17.3k
views
discrete-mathematics
kenneth-rosen
37
votes
9
answers
50
GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
Arjun
asked
in
Set Theory & Algebra
Feb 7, 2019
by
Arjun
17.2k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1-mark
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