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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 $Y, f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$
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...
go_editor
14.2k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
functions
normal
+
–
71
votes
5
answers
92
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 $\text{equivalent}$ ...
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 autom...
Kathleen
14.2k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gatecse-2008
easy
mathematical-logic
first-order-logic
+
–
9
votes
2
answers
93
Please explain this question .. Number of trivial substrings in “GATE2013” are: A. 37 B. 35 C. 2 D. 36
vijay dwivedi
14.1k
views
vijay dwivedi
asked
Jun 7, 2015
Combinatory
combinatory
counting
+
–
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
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 equ...
Kathleen
14.1k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
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
$G$ 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...
Ishrat Jahan
14.1k
views
Ishrat Jahan
asked
Oct 28, 2014
Graph Theory
gateit-2008
graph-theory
graph-connectivity
normal
+
–
40
votes
5
answers
96
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
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 transi...
Kathleen
14.0k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
relations
normal
+
–
40
votes
5
answers
97
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
What is the converse of the following assertion?I stay only if you goI stay if you goIf I stay then you goIf you do not go then I do not stayIf I do not stay then you go
Kathleen
14.0k
views
Kathleen
asked
Sep 25, 2014
Mathematical Logic
gate1998
mathematical-logic
easy
propositional-logic
+
–
7
votes
3
answers
98
ISRO2018-38
The number of edges in a regular graph of degree: $d$ and $n$ vertices is: maximum of $n$ and $d$ $n +d$ $nd$ $nd/2$
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
14.0k
views
Arjun
asked
Apr 22, 2018
Graph Theory
isro2018
graph-theory
graph-connectivity
+
–
3
votes
1
answer
99
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.
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 s...
go_editor
13.8k
views
go_editor
asked
Apr 14, 2016
Mathematical Logic
kenneth-rosen
discrete-mathematics
mathematical-logic
+
–
2
votes
7
answers
100
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 ?
In one text I read that , if n is square free it is DISTRIBUTIVEin other text I read that if n is square free it is BOOLEAN ALGEBRA .Which is most correct ?Here D36 is n...
pC
13.8k
views
pC
asked
Jun 23, 2016
Set Theory & Algebra
set-theory&algebra
lattice
+
–
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) $
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...
go_editor
13.8k
views
go_editor
asked
Sep 28, 2014
Mathematical Logic
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 _______
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
13.7k
views
Arjun
asked
Feb 12, 2020
Graph Theory
gatecse-2020
numerical-answers
graph-theory
graph-coloring
2-marks
+
–
28
votes
6
answers
103
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.
A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on $n$ vertices, $n$ isA multiple of 4EvenOddCongruent to 0 $mod$ 4...
go_editor
13.7k
views
go_editor
asked
Feb 12, 2015
Graph Theory
gatecse-2015-set2
graph-theory
graph-isomorphism
out-of-syllabus-now
+
–
0
votes
1
answer
104
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 $1s?$
How many bit strings of length $10$ containexactly four $1s?$at most four $1s?$at least four $1s?$an equal number of $0s$ and $1s?$
admin
13.6k
views
admin
asked
Apr 29, 2020
Combinatory
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
+
–
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
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 statement...
Kathleen
13.6k
views
Kathleen
asked
Sep 29, 2014
Set Theory & Algebra
gate1997
set-theory&algebra
group-theory
normal
+
–
60
votes
6
answers
106
GATE CSE 2000 | Question: 2.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
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
13.6k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2000
set-theory&algebra
easy
set-theory
+
–
8
votes
1
answer
107
Kenneth Rosen Edition 7 Exercise 1.1 Question 6 (Page No. 13)
Suppose that SmartphoneA has 256 MB RAM and 32 GB ROM, and the resolution of its camera is 8 MP; Smartphone B has 288 MB RAM and 64 GB ROM, and the resolution of its camera is 4 MP; and Smartphone C has 128 MB ... resolution camera. Smartphone A has more RAM than Smartphone B if and only if Smartphone B has more RAM than Smartphone A.
Suppose that SmartphoneA has 256 MB RAM and 32 GB ROM, and the resolution of its camera is 8 MP; Smartphone B has 288 MB RAM and 64 GB ROM, and the resolution of its came...
go_editor
13.5k
views
go_editor
asked
Apr 13, 2016
Mathematical Logic
mathematical-logic
kenneth-rosen
discrete-mathematics
+
–
60
votes
9
answers
108
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 $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
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 th...
gatecse
13.5k
views
gatecse
asked
Sep 21, 2014
Combinatory
gatecse-2005
set-theory&algebra
normal
pigeonhole-principle
+
–
8
votes
1
answer
109
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
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...
Anu
13.5k
views
Anu
asked
Jul 14, 2015
Combinatory
combinatory
counting
pigeonhole-principle
+
–
41
votes
3
answers
110
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:
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}, \overl...
Kathleen
13.5k
views
Kathleen
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2007
set-theory&algebra
normal
partial-order
descriptive
+
–
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