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Most answered questions in Discrete Mathematics
1
vote
6
answers
121
UGC NET CSE | November 2017 | Part 2 | Question: 8
Let $P$ and $Q$ be two propositions $\neg (P \leftrightarrow Q)$ is equivalent to $P\leftrightarrow \neg Q$ $\neg P\leftrightarrow Q$ $\neg P \leftrightarrow \neg Q$ $Q\rightarrow P$
Arjun
asked
in
Mathematical Logic
Nov 5, 2017
by
Arjun
2.3k
views
ugcnetcse-nov2017-paper2
discrete-mathematics
mathematical-logic
36
votes
6
answers
122
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
20
votes
6
answers
123
GATE CSE 1988 | Question: 1vii
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
go_editor
asked
in
Set Theory & Algebra
Dec 10, 2016
by
go_editor
4.6k
views
gate1988
descriptive
lattice
set-theory&algebra
21
votes
6
answers
124
GATE CSE 1989 | Question: 1-iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 27, 2016
by
makhdoom ghaya
7.1k
views
gate1989
set-theory&algebra
relations
descriptive
29
votes
6
answers
125
GATE CSE 1990 | Question: 3-x
Indicate which of the following well-formed formulae are valid: $\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)$ ...
makhdoom ghaya
asked
in
Mathematical Logic
Nov 22, 2016
by
makhdoom ghaya
9.3k
views
gate1990
normal
mathematical-logic
propositional-logic
multiple-selects
1
vote
6
answers
126
GATE Overflow | Mathematics | Test 1 | Question: 2
Four couples decide to form a committee of four members. The number of different committees that can be formed in which no couple finds a place is? 10 12 14 16
Bikram
asked
in
Combinatory
Aug 6, 2016
by
Bikram
700
views
go-mathematics-1
combinatory
19
votes
6
answers
127
CMI2013-A-06
A simple graph is one in which there are no self-loops and each pair of distinct vertices is connected by at most one edge. Let $G$ be a simple graph on $8$ vertices such that there is a vertex of degree $1$, a vertex of degree $2$, a vertex of degree $3$, a vertex ... degree $6$ and a vertex of degree $7$. Which of the following can be the degree of the last vertex? $3$ $0$ $5$ $4$
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
5.2k
views
cmi2013
graph-theory
normal
degree-of-graph
89
votes
6
answers
128
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
69
votes
6
answers
129
GATE CSE 2016 Set 2 | Question: 27
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$
Akash Kanase
asked
in
Mathematical Logic
Feb 12, 2016
by
Akash Kanase
16.8k
views
gatecse-2016-set2
mathematical-logic
first-order-logic
normal
8
votes
6
answers
130
In how many ways can the entrepreneur assign 5 different tasks to 3 employees if each should get atleast 1 task ?
radha gogia
asked
in
Combinatory
Dec 3, 2015
by
radha gogia
5.9k
views
combinatory
24
votes
6
answers
131
TIFR CSE 2012 | Part A | Question: 7
It is required to divide the $2n$ members of a club into $n$ disjoint teams of $2$ members each. The teams are not labelled. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^n . n!}$ $\frac{n!}{2}$ None of the above
makhdoom ghaya
asked
in
Combinatory
Oct 26, 2015
by
makhdoom ghaya
4.6k
views
tifr2012
combinatory
balls-in-bins
37
votes
6
answers
132
TIFR CSE 2010 | Part B | Question: 36
In a directed graph, every vertex has exactly seven edges coming in. What can one always say about the number of edges going out of its vertices? Exactly seven edges leave every vertex. Exactly seven edges leave some vertex. Some vertex has at least seven edges leaving it. The number of edges coming out of vertex is odd. None of the above.
makhdoom ghaya
asked
in
Graph Theory
Oct 10, 2015
by
makhdoom ghaya
5.9k
views
tifr2010
graph-theory
degree-of-graph
76
votes
6
answers
133
GATE CSE 2015 Set 1 | Question: 34
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram: For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \wedge y$ are join and meet of $x, y$ ... $p_r = 0$ $p_r = 1$ $0 < p_r ≤ \frac{1}{5}$ $\frac{1}{5} < p_r < 1$
makhdoom ghaya
asked
in
Set Theory & Algebra
Feb 13, 2015
by
makhdoom ghaya
17.2k
views
gatecse-2015-set1
set-theory&algebra
normal
lattice
64
votes
6
answers
134
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
28
votes
6
answers
135
GATE CSE 2015 Set 2 | Question: 28
A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on $n$ vertices, $n$ is A multiple of 4 Even Odd Congruent to 0 $mod$ 4, or, 1 $mod$ 4.
go_editor
asked
in
Graph Theory
Feb 12, 2015
by
go_editor
12.6k
views
gatecse-2015-set2
graph-theory
graph-isomorphism
out-of-syllabus-now
23
votes
6
answers
136
GATE CSE 2015 Set 2 | Question: 18
The cardinality of the power set of $\{0, 1, 2, \dots , 10\}$ is _______
go_editor
asked
in
Set Theory & Algebra
Feb 12, 2015
by
go_editor
5.1k
views
gatecse-2015-set2
set-theory&algebra
set-theory
easy
numerical-answers
33
votes
6
answers
137
GATE CSE 2015 Set 2 | Question: 3
Consider the following two statements. $S_1$: If a candidate is known to be corrupt, then he will not be elected $S_2$: If a candidate is kind, he will be elected Which one of the following statements follows from $S_1$ and $S_2$ as per sound inference ... If a person is kind, he is not known to be corrupt If a person is not kind, he is not known to be corrupt
go_editor
asked
in
Mathematical Logic
Feb 12, 2015
by
go_editor
8.8k
views
gatecse-2015-set2
mathematical-logic
normal
logical-reasoning
62
votes
6
answers
138
GATE IT 2006 | Question: 21
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
Ishrat Jahan
asked
in
Mathematical Logic
Oct 31, 2014
by
Ishrat Jahan
13.4k
views
gateit-2006
mathematical-logic
normal
first-order-logic
73
votes
6
answers
139
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
21.5k
views
gateit-2007
graph-theory
graph-connectivity
normal
43
votes
6
answers
140
GATE IT 2008 | Question: 27
$G$ is a simple undirected graph. Some vertices of $G$ are of odd degree. Add a node $v$ to $G$ and make it adjacent to each odd degree vertex of $G$. The resultant graph is sure to be regular complete Hamiltonian Euler
Ishrat Jahan
asked
in
Graph Theory
Oct 28, 2014
by
Ishrat Jahan
14.0k
views
gateit-2008
graph-theory
graph-connectivity
normal
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