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Featured
Hot questions in Discrete Mathematics
88
votes
7
answers
1
GATE CSE 2004 | Question: 23, ISRO2007-32
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
Identify the correct translation into logical notation of the following assertion.Some boys in the class are taller than all the girlsNote: $\text{taller} (x, y)$ is true...
Kathleen
131k
views
Kathleen
asked
Sep 18, 2014
Mathematical Logic
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
+
–
71
votes
5
answers
2
GATE CSE 2010 | Question: 30
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. Which one of the statements below expresses best the meaning of the formula, $\qquad∀x∃y∃t(¬F(x,y,t))$ Everyone can ... time No one can fool everyone all the time Everyone cannot fool some person all the time No one can fool some person at some time
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$.Which one of the statements below expresses best the...
gatecse
82.4k
views
gatecse
asked
Sep 21, 2014
Mathematical Logic
gatecse-2010
mathematical-logic
easy
first-order-logic
+
–
60
votes
10
answers
3
GATE CSE 2003 | Question: 36
How many perfect matching are there in a complete graph of $6$ vertices? $15$ $24$ $30$ $60$
How many perfect matching are there in a complete graph of $6$ vertices?$15$$24$$30$$60$
Kathleen
50.5k
views
Kathleen
asked
Sep 16, 2014
Graph Theory
gatecse-2003
graph-theory
graph-matching
normal
+
–
113
votes
9
answers
4
GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to$15$$30$$90$$36...
gatecse
35.0k
views
gatecse
asked
Sep 12, 2014
Graph Theory
gatecse-2012
graph-theory
normal
marks-to-all
counting
+
–
13
votes
3
answers
5
relation
Number of relations $S$ over set $\{0,1,2,3 \}$ such that $(x,y) \in S \Rightarrow x = y$
Number of relations $S$ over set $\{0,1,2,3 \}$ such that $(x,y) \in S \Rightarrow x = y$
Lakshman Bhaiya
44.5k
views
Lakshman Bhaiya
asked
Dec 27, 2017
Set Theory & Algebra
set-theory&algebra
relations
+
–
78
votes
12
answers
6
GATE CSE 1994 | Question: 1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
The number of distinct simple graphs with up to three nodes is$15$$10$$7$$9$
Kathleen
34.9k
views
Kathleen
asked
Oct 4, 2014
Graph Theory
gate1994
graph-theory
graph-connectivity
combinatory
normal
isro2008
counting
+
–
101
votes
10
answers
7
GATE CSE 2014 Set 1 | Question: 51
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $...
go_editor
26.9k
views
go_editor
asked
Sep 28, 2014
Graph Theory
gatecse-2014-set1
graph-theory
numerical-answers
normal
graph-connectivity
+
–
39
votes
9
answers
8
GATE CSE 2014 Set 2 | Question: 3
The maximum number of edges in a bipartite graph on $12$ vertices is____
The maximum number of edges in a bipartite graph on $12$ vertices is____
go_editor
27.2k
views
go_editor
asked
Sep 28, 2014
Graph Theory
gatecse-2014-set2
graph-theory
graph-connectivity
numerical-answers
normal
+
–
102
votes
11
answers
9
GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
Consider the following expressions:$false$$Q$$true$$P\vee Q$$\neg Q\vee P$The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$...
Akash Kanase
20.1k
views
Akash Kanase
asked
Feb 12, 2016
Mathematical Logic
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
+
–
92
votes
9
answers
10
GATE CSE 2016 Set 1 | Question: 28
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)...
Sandeep Singh
21.7k
views
Sandeep Singh
asked
Feb 12, 2016
Set Theory & Algebra
gatecse-2016-set1
set-theory&algebra
functions
normal
numerical-answers
+
–
33
votes
14
answers
11
GATE CSE 2019 | Question: 12
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$
Let $G$ be an undirected complete graph on $n$ vertices, where $n 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to$n!$$(n-1)!$$1$$\frac{(n-1)!}{2}...
Arjun
21.4k
views
Arjun
asked
Feb 7, 2019
Graph Theory
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
1-mark
+
–
42
votes
9
answers
12
GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
Which one of the following predicate formulae is NOT logically valid?Note that $W$ is a predicate formula without any free occurrence of $x$.$\forall x (p(x) \vee W) \equ...
Arjun
17.3k
views
Arjun
asked
Feb 12, 2020
Mathematical Logic
gatecse-2020
first-order-logic
mathematical-logic
2-marks
+
–
88
votes
5
answers
13
GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$$( \forall x \,...
go_editor
21.0k
views
go_editor
asked
Feb 13, 2015
Mathematical Logic
gatecse-2015-set2
mathematical-logic
normal
first-order-logic
+
–
57
votes
17
answers
14
GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
Sandeep Singh
25.9k
views
Sandeep Singh
asked
Feb 12, 2016
Combinatory
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
+
–
73
votes
8
answers
15
GATE CSE 2017 Set 1 | Question: 02
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ IV only I and IV only II only II and III only
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$?$\exists y(\ex...
khushtak
17.3k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
first-order-logic
+
–
34
votes
6
answers
16
GATE CSE 1996 | Question: 1.4
Which of the following statements is FALSE? The set of rational numbers is an abelian group under addition The set of integers in an abelian group under addition The set of rational numbers form an abelian group under multiplication The set of real numbers excluding zero is an abelian group under multiplication
Which of the following statements is FALSE?The set of rational numbers is an abelian group under additionThe set of integers in an abelian group under additionThe set of ...
Kathleen
23.1k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
group-theory
normal
+
–
19
votes
18
answers
17
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
The value of $3^{51} \text{ mod } 5$ is _____
Arjun
18.3k
views
Arjun
asked
Feb 7, 2019
Combinatory
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
+
–
33
votes
9
answers
18
GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
makhdoom ghaya
24.7k
views
makhdoom ghaya
asked
Feb 13, 2015
Graph Theory
gatecse-2015-set1
graph-theory
graph-connectivity
normal
graph-planarity
numerical-answers
+
–
55
votes
6
answers
19
GATE CSE 1997 | Question: 6.3
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
The number of equivalence relations of the set $\{1,2,3,4\}$ is$15$$16$$24$$4$
Kathleen
21.4k
views
Kathleen
asked
Sep 29, 2014
Set Theory & Algebra
gate1997
set-theory&algebra
relations
normal
+
–
52
votes
15
answers
20
GATE CSE 2015 Set 2 | Question: 40
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
go_editor
19.5k
views
go_editor
asked
Feb 12, 2015
Set Theory & Algebra
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
+
–
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