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Hot questions in Discrete Mathematics
58
votes
7
answers
41
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
49.7k
views
gateit-2008
normal
graph-connectivity
24
votes
6
answers
42
GATE CSE 1995 | Question: 1.20
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is: $2$ $4$ $8$ None of the above
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
16.2k
views
gate1995
set-theory&algebra
normal
set-theory
77
votes
6
answers
43
GATE CSE 2014 Set 3 | Question: 50
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
15.5k
views
gatecse-2014-set3
set-theory&algebra
group-theory
numerical-answers
normal
66
votes
10
answers
44
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
64
votes
6
answers
45
GATE CSE 2015 Set 1 | Question: 16
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\varnothing \in 2^{A}$ $\varnothing \subseteq 2^{A}$ ... I and III only II and III only I, II and III only I, II and IV only
makhdoom ghaya
asked
in
Set Theory & Algebra
Feb 13, 2015
by
makhdoom ghaya
15.5k
views
gatecse-2015-set1
set-theory&algebra
set-theory
normal
50
votes
9
answers
46
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Ishrat Jahan
asked
in
Mathematical Logic
Nov 3, 2014
by
Ishrat Jahan
14.7k
views
gateit-2005
mathematical-logic
first-order-logic
normal
73
votes
6
answers
47
GATE IT 2007 | Question: 25
What is the largest integer $m$ such that every simple connected graph with $n$ vertices and $n$ edges contains at least $m$ different spanning trees ? $1$ $2$ $3$ $n$
Ishrat Jahan
asked
in
Graph Theory
Oct 29, 2014
by
Ishrat Jahan
21.4k
views
gateit-2007
graph-theory
graph-connectivity
normal
71
votes
7
answers
48
GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.
Sandeep Singh
asked
in
Mathematical Logic
Feb 12, 2016
by
Sandeep Singh
12.9k
views
gatecse-2016-set1
mathematical-logic
normal
numerical-answers
propositional-logic
68
votes
9
answers
49
GATE IT 2008 | Question: 21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
Ishrat Jahan
asked
in
Mathematical Logic
Oct 27, 2014
by
Ishrat Jahan
15.1k
views
gateit-2008
first-order-logic
normal
5
votes
2
answers
50
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
7
votes
4
answers
51
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
admin
asked
in
Combinatory
Feb 15, 2023
by
admin
7.8k
views
gatecse-2023
combinatory
recurrence-relation
1-mark
62
votes
10
answers
52
GATE CSE 2002 | Question: 1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
Kathleen
asked
in
Mathematical Logic
Sep 15, 2014
by
Kathleen
14.7k
views
gatecse-2002
mathematical-logic
normal
propositional-logic
70
votes
5
answers
53
GATE CSE 2008 | Question: 30
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown automaton. Let $\text{equivalent}$ ...
Kathleen
asked
in
Mathematical Logic
Sep 12, 2014
by
Kathleen
14.0k
views
gatecse-2008
easy
mathematical-logic
first-order-logic
65
votes
9
answers
54
GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$
Kathleen
asked
in
Graph Theory
Sep 17, 2014
by
Kathleen
15.6k
views
gatecse-2003
graph-theory
normal
degree-of-graph
36
votes
6
answers
55
GATE CSE 2017 Set 2 | Question: 21
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
khushtak
asked
in
Set Theory & Algebra
Feb 14, 2017
by
khushtak
11.8k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
59
votes
8
answers
56
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
19.1k
views
gatecse-2013
graph-theory
normal
graph-connectivity
65
votes
16
answers
57
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 ________.
go_editor
asked
in
Combinatory
Feb 14, 2015
by
go_editor
15.6k
views
gatecse-2015-set3
combinatory
normal
numerical-answers
66
votes
10
answers
58
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
50
votes
8
answers
59
GATE CSE 2016 Set 2 | Question: 26
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? ... and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
Akash Kanase
asked
in
Set Theory & Algebra
Feb 12, 2016
by
Akash Kanase
14.6k
views
gatecse-2016-set2
set-theory&algebra
relations
normal
65
votes
5
answers
60
GATE CSE 2003 | Question: 8, ISRO2009-53
Let $\text{G}$ be an arbitrary graph with $n$ nodes and $k$ components. If a vertex is removed from $\text{G}$, the number of components in the resultant graph must necessarily lie down between $k$ and $n$ $k-1$ and $k+1$ $k-1$ and $n-1$ $k+1$ and $n-k$
Kathleen
asked
in
Graph Theory
Sep 16, 2014
by
Kathleen
15.3k
views
gatecse-2003
graph-theory
graph-connectivity
normal
isro2009
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