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Most viewed questions in Discrete Mathematics
63
votes
5
answers
91
GATE CSE 2014 Set 3 | Question: 2
Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE? For any subsets $A$ and $B$ of $X, |f(A \cup B)| = |f(A)| + |f(B)|$ For any subsets $A$ and $B$ of $X, f(A \cap B) = f(A) \cap f(B)$ For any subsets $A$ ... $S$ and $T$ of $Y, f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
14.0k
views
gatecse-2014-set3
set-theory&algebra
functions
normal
52
votes
6
answers
92
GATE CSE 2001 | Question: 2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $
Kathleen
asked
in
Graph Theory
Sep 14, 2014
by
Kathleen
14.0k
views
gatecse-2001
graph-theory
normal
counting
70
votes
5
answers
93
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
39
votes
5
answers
94
GATE CSE 2000 | Question: 2.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having $1$ equivalence class $R$ is an equivalence relation having $2$ equivalence classes $R$ is an equivalence relation having $3$ equivalence classes
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
14.0k
views
gatecse-2000
set-theory&algebra
relations
normal
43
votes
6
answers
95
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
13.9k
views
gateit-2008
graph-theory
graph-connectivity
normal
7
votes
3
answers
96
ISRO2018-38
The number of edges in a regular graph of degree: $d$ and $n$ vertices is: maximum of $n$ and $d$ $n +d$ $nd$ $nd/2$
Arjun
asked
in
Graph Theory
Apr 22, 2018
by
Arjun
13.9k
views
isro2018
graph-theory
graph-connectivity
40
votes
5
answers
97
GATE CSE 1996 | Question: 2.2
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
13.9k
views
gate1996
set-theory&algebra
relations
normal
39
votes
5
answers
98
GATE CSE 1998 | Question: 1.5
What is the converse of the following assertion? I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go
Kathleen
asked
in
Mathematical Logic
Sep 25, 2014
by
Kathleen
13.8k
views
gate1998
mathematical-logic
easy
propositional-logic
2
votes
7
answers
99
is D36 distributive ?
In one text I read that , if n is square free it is DISTRIBUTIVE in other text I read that if n is square free it is BOOLEAN ALGEBRA . Which is most correct ? Here D36 is not square free then... what conclusion can I make ?
pC
asked
in
Set Theory & Algebra
Jun 23, 2016
by
pC
13.7k
views
set-theory&algebra
lattice
3
votes
1
answer
100
Kenneth Rosen Edition 6th Exercise 1.1 Question 24 (Page No. 19)
State the converse, contrapositive, and inverse of each of these conditional statements. If it snows tonight, then I will stay at home. I go to the beach whenever it is a sunny summer day. When I stay up late, it is necessary that I sleep until noon.
go_editor
asked
in
Mathematical Logic
Apr 14, 2016
by
go_editor
13.6k
views
kenneth-rosen
discrete-mathematics
mathematical-logic
51
votes
12
answers
101
GATE CSE 2014 Set 1 | Question: 53
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ ... $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
13.5k
views
gatecse-2014-set1
mathematical-logic
normal
propositional-logic
28
votes
6
answers
102
GATE CSE 2020 | Question: 52
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is _______
Arjun
asked
in
Graph Theory
Feb 12, 2020
by
Arjun
13.5k
views
gatecse-2020
numerical-answers
graph-theory
graph-coloring
2-marks
60
votes
6
answers
103
GATE CSE 2000 | Question: 2.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
13.4k
views
gatecse-2000
set-theory&algebra
easy
set-theory
22
votes
5
answers
104
GATE CSE 1996 | Question: 1.2
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is $3$ $4$ $9$ None of the above
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
13.4k
views
gate1996
set-theory&algebra
partial-order
normal
24
votes
6
answers
105
GATE CSE 1997 | Question: 3.1
Let $\left(Z, *\right)$ be an algebraic structure where $Z$ is the set of integers and the operation $*$ is defined by $n*m = \max(n,m)$. Which of the following statements is true for $\left(Z, *\right)$? $\left(Z, *\right)$ is a monoid $\left(Z, *\right)$ is an Abelian group $\left(Z, *\right)$ is a group None of the above
Kathleen
asked
in
Set Theory & Algebra
Sep 29, 2014
by
Kathleen
13.4k
views
gate1997
set-theory&algebra
group-theory
normal
0
votes
1
answer
106
Kenneth Rosen Edition 7 Exercise 6.3 Question 11 (Page No. 413)
How many bit strings of length $10$ contain exactly four $1s?$ at most four $1s?$ at least four $1s?$ an equal number of $0s$ and $1s?$
admin
asked
in
Combinatory
Apr 29, 2020
by
admin
13.4k
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
44
votes
4
answers
107
GATE CSE 2003 | Question: 4
Let $A$ be a sequence of $8$ distinct integers sorted in ascending order. How many distinct pairs of sequences, $B$ and $C$ are there such that each is sorted in ascending order, $B$ has $5$ and $C$ has $3$ elements, and the result of merging $B$ and $C$ gives $A$ $2$ $30$ $56$ $256$
Kathleen
asked
in
Combinatory
Sep 16, 2014
by
Kathleen
13.3k
views
gatecse-2003
combinatory
normal
8
votes
1
answer
108
application of pigeonhole principle
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days during which the team must play exactly 14 games
Anu
asked
in
Combinatory
Jul 14, 2015
by
Anu
13.3k
views
combinatory
counting
pigeonhole-principle
41
votes
3
answers
109
GATE CSE 2007 | Question: 26
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:
Kathleen
asked
in
Set Theory & Algebra
Sep 21, 2014
by
Kathleen
13.3k
views
gatecse-2007
set-theory&algebra
normal
partial-order
descriptive
60
votes
9
answers
110
GATE CSE 2005 | Question: 44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
gatecse
asked
in
Combinatory
Sep 21, 2014
by
gatecse
13.3k
views
gatecse-2005
set-theory&algebra
normal
pigeonhole-principle
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