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Hot questions in Discrete Mathematics
13
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1
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151
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 15
Let $\mathrm{G}$ be a simple undirected 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 of degree 4, a vertex of degree 5 , a vertex of degree 6 and ... of degree 7. Which of the following can be the degree of the last vertex? (Select all that are possible) 0 3 4 8
GO Classes
asked
in
Graph Theory
Feb 5
by
GO Classes
565
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goclasses2024-mockgate-14
graph-theory
degree-of-graph
multiple-selects
1-mark
10
votes
1
answer
152
GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.
admin
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in
Set Theory & Algebra
Feb 15, 2023
by
admin
5.5k
views
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
34
votes
6
answers
153
GATE CSE 2004 | Question: 24
Consider the binary relation: $S= \left\{\left(x, y\right) \mid y=x+1 \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$ The reflexive transitive closure is $S$ ... $\left\{\left(x, y\right) \mid y \leq x \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$
Kathleen
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in
Set Theory & Algebra
Sep 18, 2014
by
Kathleen
9.8k
views
gatecse-2004
set-theory&algebra
easy
relations
41
votes
3
answers
154
GATE CSE 1994 | Question: 1.10
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$? $g=g^{-1} \text{ for every } g \in G$ $g=g^2 \text{ for every }g \in G$ $(goh)^2 = g^2oh^2 \text{ for every } g, h \in G$ $G$ is of finite order
Kathleen
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in
Set Theory & Algebra
Oct 4, 2014
by
Kathleen
10.6k
views
gate1994
set-theory&algebra
group-theory
normal
10
votes
1
answer
155
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 45
Below is a drawing(graph representation) of a binary relation $\text{R}$ over a set $\text{P}$ of elements $\{ \text{A, B, C, D, E, F}\}:$ Which of the following first-order logic statements about $\mathrm{R}$ ... $\forall x \in P . \exists y \in P . x R y$
GO Classes
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in
Mathematical Logic
Jan 21
by
GO Classes
581
views
goclasses2024-mockgate-12
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
43
votes
8
answers
156
GATE CSE 2007 | Question: 22
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ ... $\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$
Kathleen
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in
Mathematical Logic
Sep 21, 2014
by
Kathleen
8.8k
views
gatecse-2007
mathematical-logic
easy
first-order-logic
43
votes
7
answers
157
GATE CSE 2015 Set 3 | Question: 41
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about $R$? Both reflexive and symmetric Reflexive but not symmetric Not reflexive but symmetric Neither reflexive nor symmetric
go_editor
asked
in
Set Theory & Algebra
Feb 15, 2015
by
go_editor
12.8k
views
gatecse-2015-set3
set-theory&algebra
relations
normal
43
votes
2
answers
158
GATE CSE 1989 | Question: 1-v
The number of possible commutative binary operations that can be defined on a set of $n$ elements (for a given $n$) is ___________.
makhdoom ghaya
asked
in
Set Theory & Algebra
Nov 27, 2016
by
makhdoom ghaya
6.5k
views
gate1989
descriptive
set-theory&algebra
binary-operation
27
votes
4
answers
159
GATE CSE 1995 | Question: 2.17
Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then $A$ is closed under $*$ but $\langle A, *\rangle$ is not a semigroup. $\langle A, *\rangle$ is a semigroup but not a monoid. $\langle A, * \rangle$ is a monoid but not a group. $\langle A, *\rangle$ is a a group but not an abelian group.
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
9.8k
views
gate1995
set-theory&algebra
group-theory
6
votes
2
answers
160
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 56
The coefficient of $x^6$ in the expansion of $A(x)$ is, where $ A(x)=\frac{x(1+x)}{(1-x)^3} $
GO Classes
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in
Combinatory
Feb 5
by
GO Classes
500
views
goclasses2024-mockgate-14
numerical-answers
combinatory
recurrence-relation
2-marks
6
votes
1
answer
161
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 57
A strongly connected component $(\mathrm{SCC})$ of a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$ ... ; edges in its associated directed acyclic graph $G^{\prime}$ be $A, B$ respectively, then what is $A+B?$
GO Classes
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in
Graph Theory
Feb 5
by
GO Classes
495
views
goclasses2024-mockgate-14
numerical-answers
graph-theory
graph-connectivity
2-marks
40
votes
7
answers
162
GATE CSE 2005 | Question: 43
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto
gatecse
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Set Theory & Algebra
Sep 21, 2014
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gatecse
9.9k
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gatecse-2005
set-theory&algebra
functions
normal
0
votes
1
answer
163
GATE CSE 2024 | Set 1 | Question: 41
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic number $k$. Which of the following statements is/are always TRUE? $G$ contains a complete subgraph with ... $n/k$ $G$ contains at least $k(k-1) / 2$ edges $G$ contains a vertex of degree at least $k$
Arjun
asked
in
Graph Theory
Feb 16
by
Arjun
1.8k
views
gatecse2024-set1
multiple-selects
graph-theory
45
votes
4
answers
164
GATE CSE 1996 | Question: 2.4
Which one of the following is false? The set of all bijective functions on a finite set forms a group under function composition The set $\{1, 2, \dots p-1\}$ forms a group under multiplication mod $p$, where $p$ is a prime number The set of all strings over a finite ... $\langle G, * \rangle$ if and only if for any pair of elements $a, b \in S, a * b^{-1} \in S$
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
9.5k
views
gate1996
set-theory&algebra
normal
set-theory
group-theory
7
votes
2
answers
165
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 44
Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the last character must be a digit, and any character that is a sign must be followed by a digit. There ... by $N_k=a N _{k-1}+b N _{k-2}$, for $k \geq 3$. What is $a+ b?$
GO Classes
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in
Combinatory
Jan 13
by
GO Classes
533
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goclasses2024-mockgate-11
goclasses
numerical-answers
combinatory
recurrence-relation
2-marks
8
votes
1
answer
166
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 12
Let $A-B$ denote $\{x \in A: x \notin B\}$. If $(A-B) \cup B=A$, which of the following must be true? $B$ is empty $A \subseteq B$ $B \subseteq A$ $(B-A) \cup A=B$
GO Classes
asked
in
Set Theory & Algebra
Jan 13
by
GO Classes
626
views
goclasses2024-mockgate-11
goclasses
set-theory&algebra
set-theory
1-mark
6
votes
2
answers
167
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 17
The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the piles are also distinguishable?
GO Classes
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in
Combinatory
Jan 21
by
GO Classes
862
views
goclasses2024-mockgate-12
goclasses
numerical-answers
combinatory
counting
1-mark
8
votes
1
answer
168
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 38
A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y R z$. Which of the following ... is transitive. If $R$ is a GO relation then $R$ is reflexive. If $R$ is an equivalence relation then $R$ is a GO relation.
GO Classes
asked
in
Set Theory & Algebra
Jan 13
by
GO Classes
550
views
goclasses2024-mockgate-11
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
4
votes
1
answer
169
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 46
Assume the following graph is a labeled graph i.e. every vertex has a unique label. In how many ways can we color the following labeled graph $\mathrm{G}$ with six colors $\{R, G, B, W, Y, M\}$ such that no two adjacent vertices are assigned the same color?
GO Classes
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in
Graph Theory
Jan 21
by
GO Classes
581
views
goclasses2024-mockgate-12
goclasses
numerical-answers
graph-theory
graph-coloring
2-marks
0
votes
1
answer
170
Discrete mathematics Ch 1 : Propositional logic , Topic 2 : Logical operators or connectives
Which of the following is the negation of x is even iff x is divisible by 2 a) (x is even or x is not divisible by 2) and (x is not even or x is divisible by 2) b) (x is even and x is not divisible by 2) ... is divisible by 2) c) x is not even iff x is not divisible by 2 d) x is even if x is divisible by 2
lipishagupta
asked
in
Mathematical Logic
Mar 20
by
lipishagupta
60
views
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