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Most viewed questions in Discrete Mathematics
1
vote
3
answers
61
k 3,4 graph
The graph $K_{3,4}$ has 3 edges 4 edges 7 edges 12 edges
Sanjay Sharma
asked
in
Graph Theory
Jun 3, 2016
by
Sanjay Sharma
16.4k
views
78
votes
6
answers
62
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
Arjun
asked
in
Mathematical Logic
Sep 2, 2014
by
Arjun
16.3k
views
gate1992
mathematical-logic
normal
first-order-logic
10
votes
3
answers
63
ISRO2007-29
The set of all Equivalence Classes of a set A of Cardinality C is of cardinality $2^c$ have the same cardinality as A forms a partition of A is of cardinality $C^2$
go_editor
asked
in
Set Theory & Algebra
Jun 10, 2016
by
go_editor
16.3k
views
isro2007
set-theory&algebra
equivalence-class
24
votes
6
answers
64
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
25
votes
2
answers
65
GATE CSE 2013 | Question: 25
Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. P only Q only Both P and Q Neither P nor Q
Arjun
asked
in
Graph Theory
Sep 24, 2014
by
Arjun
15.9k
views
gatecse-2013
graph-theory
easy
degree-of-graph
77
votes
8
answers
66
GATE CSE 2014 Set 2 | Question: 50
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the ... $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
15.8k
views
gatecse-2014-set2
set-theory&algebra
normal
set-theory
113
votes
6
answers
67
GATE CSE 2003 | Question: 33
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: ... I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
Kathleen
asked
in
Mathematical Logic
Sep 16, 2014
by
Kathleen
15.7k
views
gatecse-2003
mathematical-logic
difficult
first-order-logic
65
votes
9
answers
68
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
6
votes
1
answer
69
The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain a) exactly one vowel? b) exactly two vowels? c) at least one vowel? d) at least two vowels?
Sahil Gupta
asked
in
Combinatory
Nov 23, 2014
by
Sahil Gupta
15.5k
views
78
votes
6
answers
70
GATE CSE 2014 Set 3 | Question: 49
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$. For each such function it must be the case that for every ... is CORRECT? $P, Q$ and $R$ are true Only $Q$ and $R$ are true Only $P$ and $Q$ are true Only $R$ is true
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
15.5k
views
gatecse-2014-set3
set-theory&algebra
functions
normal
65
votes
16
answers
71
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
15.5k
views
gatecse-2015-set3
combinatory
normal
numerical-answers
77
votes
6
answers
72
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
64
votes
6
answers
73
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
15.4k
views
gatecse-2015-set1
set-theory&algebra
set-theory
normal
43
votes
4
answers
74
GATE CSE 2016 Set 2 | Question: 03
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________.
Akash Kanase
asked
in
Graph Theory
Feb 12, 2016
by
Akash Kanase
15.4k
views
gatecse-2016-set2
graph-theory
graph-coloring
normal
numerical-answers
65
votes
5
answers
75
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
68
votes
9
answers
76
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
15.0k
views
gateit-2008
first-order-logic
normal
33
votes
8
answers
77
GATE IT 2008 | Question: 28
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only
Ishrat Jahan
asked
in
Set Theory & Algebra
Oct 28, 2014
by
Ishrat Jahan
14.9k
views
gateit-2008
set-theory&algebra
lattice
normal
1
vote
1
answer
78
How many equivalence classes can be made form {1,2,3}?
How many equivalence classes can be made form {1,2,3}? a. 3 b. 5 c. 7 d. 8 How to solve this type of Questions?
sh!va
asked
in
Set Theory & Algebra
Jul 1, 2016
by
sh!va
14.8k
views
set-theory&algebra
relations
50
votes
9
answers
79
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
62
votes
10
answers
80
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
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