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Most viewed questions in Discrete Mathematics
87
votes
7
answers
1
GATE CSE 2004 | Question: 23, ISRO2007-32
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
Kathleen
asked
in
Mathematical Logic
Sep 18, 2014
by
Kathleen
110k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
69
votes
5
answers
2
GATE CSE 2010 | Question: 30
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. Which one of the statements below expresses best the meaning of the formula, $\qquad∀x∃y∃t(¬F(x,y,t))$ Everyone can ... time No one can fool everyone all the time Everyone cannot fool some person all the time No one can fool some person at some time
gatecse
asked
in
Mathematical Logic
Sep 21, 2014
by
gatecse
70.0k
views
gatecse-2010
mathematical-logic
easy
first-order-logic
39
votes
7
answers
3
GATE CSE 2008 | Question: 23
Which of the following statements is true for every planar graph on $n$ vertices? The graph is connected The graph is Eulerian The graph has a vertex-cover of size at most $\frac{3n}{4}$ The graph has an independent set of size at least $\frac{n}{3}$
Kathleen
asked
in
Graph Theory
Sep 11, 2014
by
Kathleen
55.0k
views
gatecse-2008
graph-theory
normal
graph-planarity
58
votes
7
answers
4
GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$
Ishrat Jahan
asked
in
Graph Theory
Oct 27, 2014
by
Ishrat Jahan
49.6k
views
gateit-2008
normal
graph-connectivity
5
votes
2
answers
5
How many transitive relations are there on a set with n elements if a)n=1 b) n=2 c) n=3
How many transitive relations are there on a set with n elements if a)n=1 b) n=2 c) n=3
Sanjay Sharma
asked
in
Set Theory & Algebra
Mar 7, 2017
by
Sanjay Sharma
46.4k
views
13
votes
3
answers
6
relation
Number of relations $S$ over set $\{0,1,2,3 \}$ such that $(x,y) \in S \Rightarrow x = y$
Lakshman Bhaiya
asked
in
Set Theory & Algebra
Dec 27, 2017
by
Lakshman Bhaiya
44.5k
views
set-theory&algebra
relations
60
votes
9
answers
7
GATE CSE 2003 | Question: 36
How many perfect matching are there in a complete graph of $6$ vertices? $15$ $24$ $30$ $60$
Kathleen
asked
in
Graph Theory
Sep 16, 2014
by
Kathleen
43.8k
views
gatecse-2003
graph-theory
graph-matching
normal
111
votes
9
answers
8
GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$
gatecse
asked
in
Graph Theory
Sep 12, 2014
by
gatecse
34.7k
views
gatecse-2012
graph-theory
normal
marks-to-all
counting
76
votes
12
answers
9
GATE CSE 1994 | Question: 1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
Kathleen
asked
in
Graph Theory
Oct 4, 2014
by
Kathleen
34.6k
views
gate1994
graph-theory
graph-connectivity
combinatory
normal
isro2008
counting
1
vote
1
answer
10
Graph
1. Suppose that G is a non-directed graph with 12 edges. Suppose that G has 6 vertices of degree 3 and the rest have degrees less than 3. The minimum number of vertices G can have? a) 2 b) 0 c)1 d)3 I am getting 3..plz verify
cse23
asked
in
Graph Theory
Jan 20, 2017
by
cse23
33.1k
views
66
votes
10
answers
11
GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Sandeep Singh
asked
in
Combinatory
Feb 12, 2016
by
Sandeep Singh
28.1k
views
gatecse-2016-set1
combinatory
recurrence-relation
normal
numerical-answers
38
votes
9
answers
12
GATE CSE 2014 Set 2 | Question: 3
The maximum number of edges in a bipartite graph on $12$ vertices is____
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
26.9k
views
gatecse-2014-set2
graph-theory
graph-connectivity
numerical-answers
normal
100
votes
10
answers
13
GATE CSE 2014 Set 1 | Question: 51
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
26.7k
views
gatecse-2014-set1
graph-theory
numerical-answers
normal
graph-connectivity
19
votes
2
answers
14
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric? Please explain how to calculate .
shree
asked
in
Set Theory & Algebra
Oct 24, 2014
by
shree
25.9k
views
set-theory&algebra
relations
57
votes
17
answers
15
GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
Sandeep Singh
asked
in
Combinatory
Feb 12, 2016
by
Sandeep Singh
25.7k
views
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
76
votes
5
answers
16
GATE CSE 2007 | Question: 23
Which of the following graphs has an Eulerian circuit? Any $k$-regular graph where $k$ is an even number. A complete graph on $90$ vertices. The complement of a cycle on $25$ vertices. None of the above
Kathleen
asked
in
Graph Theory
Sep 21, 2014
by
Kathleen
25.2k
views
gatecse-2007
graph-theory
normal
graph-connectivity
36
votes
6
answers
17
GATE CSE 2005 | Question: 7
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
Kathleen
asked
in
Set Theory & Algebra
Sep 22, 2014
by
Kathleen
24.5k
views
gatecse-2005
set-theory&algebra
normal
relations
32
votes
9
answers
18
GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
makhdoom ghaya
asked
in
Graph Theory
Feb 13, 2015
by
makhdoom ghaya
24.5k
views
gatecse-2015-set1
graph-theory
graph-connectivity
normal
graph-planarity
numerical-answers
76
votes
6
answers
19
GATE CSE 2008 | Question: 42
$G$ is a graph on $n$ vertices and $2n-2$ edges. The edges of $G$ can be partitioned into two edge-disjoint spanning trees. Which of the following is NOT true for $G$? For every subset of $k$ vertices, the induced subgraph has at ... least $2$ edge-disjoint paths between every pair of vertices. There are at least $2$ vertex-disjoint paths between every pair of vertices.
Akshay Jindal
asked
in
Graph Theory
Sep 27, 2014
by
Akshay Jindal
23.4k
views
gatecse-2008
graph-connectivity
normal
33
votes
6
answers
20
GATE CSE 1996 | Question: 1.4
Which of the following statements is FALSE? The set of rational numbers is an abelian group under addition The set of integers in an abelian group under addition The set of rational numbers form an abelian group under multiplication The set of real numbers excluding zero is an abelian group under multiplication
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
22.8k
views
gate1996
set-theory&algebra
group-theory
normal
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