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Hot questions in Discrete Mathematics
41
votes
9
answers
151
GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which ...
Kathleen
9.3k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
+
–
12
votes
3
answers
152
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 58
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae. Which of the following is/are True? If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology. If $F \wedge G$ is a contradiction then at ... $G$ is a tautology. If $F \rightarrow G$ is a contradiction then $F$ is a tautology and $G$ is a contradiction.
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae.Which of the following is/are True?If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology...
GO Classes
921
views
GO Classes
asked
Feb 5
Mathematical Logic
goclasses2024-mockgate-14
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
40
votes
7
answers
153
GATE CSE 2010 | Question: 28
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph? $7, 6, 5, 4, 4, 3, 2, 1$ $6, 6, 6, 6, 3, 3, 2, 2$ $7, 6, 6, 4, 4, 3, 2, 2$ $8, 7, 7, 6, 4, 2, 1, 1$ I and II III and IV IV only II and IV
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree...
gatecse
18.7k
views
gatecse
asked
Sep 21, 2014
Graph Theory
gatecse-2010
graph-theory
degree-of-graph
+
–
13
votes
2
answers
154
GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 7
Power set of empty set has exactly _______ subsets. One Two Zero Three
Power set of empty set has exactly _______ subsets.OneTwoZeroThree
GO Classes
377
views
GO Classes
asked
Apr 3
Set Theory & Algebra
goclasses2025_cs_wq4
goclasses
set-theory&algebra
set-theory
2-marks
+
–
43
votes
8
answers
155
GATE CSE 2006 | Question: 73
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 number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$
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 set...
go_editor
9.2k
views
go_editor
asked
Apr 24, 2016
Graph Theory
gatecse-2006
graph-theory
normal
graph-connectivity
+
–
20
votes
2
answers
156
GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 8
Which of the following is/are true? If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$. If $S$ is a set and $|S| = 103$, then $S$ is a power set ... $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.
Which of the following is/are true?If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.If ...
GO Classes
476
views
GO Classes
asked
Apr 3
Set Theory & Algebra
goclasses2025_cs_wq4
goclasses
set-theory&algebra
set-theory
power-set
multiple-selects
2-marks
+
–
22
votes
6
answers
157
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 9
Which of the following statements is/are true? The argument form with premises $p_1, p_2, \ldots, p_n$ and conclusion $q \rightarrow r$ is valid iff the argument form with premises $p_1, p_2, \ldots, p_n, r$ ... the argument form with premises $p_1, p_2, \ldots, p_n, \sim r$, and conclusion $\sim q$ is valid.
Which of the following statements is/are true?The argument form with premises $p_1, p_2, \ldots, p_n$ and conclusion $q \rightarrow r$ is valid iff the argument form with...
GO Classes
1.6k
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
23
votes
2
answers
158
GATE CSE 1999 | Question: 1.2
The number of binary relations on a set with $n$ elements is: $n^2$ $2^n$ $2^{n^2}$ None of the above
The number of binary relations on a set with $n$ elements is:$n^2$$2^n$$2^{n^2}$None of the above
Kathleen
11.4k
views
Kathleen
asked
Sep 23, 2014
Set Theory & Algebra
gate1999
set-theory&algebra
relations
combinatory
easy
+
–
65
votes
9
answers
159
GATE CSE 2004 | Question: 75
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $k$ that satisfies this requirement? $9$ $8$ $7$ $6$
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pa...
Kathleen
16.9k
views
Kathleen
asked
Sep 18, 2014
Combinatory
gatecse-2004
combinatory
+
–
45
votes
4
answers
160
GATE IT 2006 | Question: 2
For the set $N$ of natural numbers and a binary operation $f : N \times N \to N,$ an element $z \in N$ is called an identity for $f,$ if $f (a, z) = a = f(z, a),$ for all $a \in N.$ Which of the following binary operations have an identity? $f (x, y) = x + y - 3$ $f (x, y) = \max(x, y)$ $f (x, y) = x^y$ I and II only II and III only I and III only None of these
For the set $N$ of natural numbers and a binary operation $f : N \times N \to N,$ an element $z \in N$ is called an identity for $f,$ if $f (a, z) = a = f(z, a),$ for all...
Ishrat Jahan
9.8k
views
Ishrat Jahan
asked
Oct 30, 2014
Set Theory & Algebra
gateit-2006
set-theory&algebra
easy
binary-operation
+
–
36
votes
5
answers
161
GATE CSE 2007 | Question: 85
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. Suppose that the robot is not allowed to traverse the ... $^{20}\mathrm{C}_{10} - ^{8}\mathrm{C}_{4}\times ^{11}\mathrm{C}_{5}$
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move...
go_editor
9.7k
views
go_editor
asked
Apr 23, 2016
Combinatory
gatecse-2007
combinatory
normal
discrete-mathematics
+
–
26
votes
6
answers
162
GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 15
Consider the following popular puzzle. A boy and a girl are talking. One of them has black hair, another has white hair. I am a boy said the child with black hair. I am a girl said the child with white hair ... Which of them is lying? The boy only The girl only Both of them Information is not sufficient to find out the liar
Consider the following popular puzzle.A boy and a girl are talking. One of them has black hair, another has white hair.“I am a boy” said the child with black hair.“...
GO Classes
1.7k
views
GO Classes
asked
Mar 30, 2022
Mathematical Logic
goclasses
goclasses2025_cs_wq1
mathematical-logic
propositional-logic
2-marks
+
–
2
votes
2
answers
163
GATE CSE 2024 | Set 2 | Question: 53
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ that are their own inverses is ___________.
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \ti...
Arjun
2.3k
views
Arjun
asked
Feb 16
Set Theory & Algebra
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
+
–
46
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 $a, b \in S, a * b^{-1} \in S$
Which one of the following is false?The set of all bijective functions on a finite set forms a group under function compositionThe set $\{1, 2, \dots p-1\}$ forms a group...
Kathleen
9.7k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
normal
set-theory
group-theory
+
–
13
votes
1
answer
165
GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 10
Which of the following statements is /are False? $\{2,3,4\} \in A$ and $\{2,3\} \in B$ implies that $\{4\} \subseteq A-B$. $A \cap B \supseteq\{2,3,4\}$ implies that $\{2,3,4\} \subseteq A$ and $\{2,3,4\} \subseteq B$ ... $\{2,3\} \subseteq A \cup B$ implies that if $\{2,3\} \cap A=\emptyset$ then $\{2,3\} \subseteq B$.
Which of the following statements is /are False?$\{2,3,4\} \in A$ and $\{2,3\} \in B$ implies that $\{4\} \subseteq A-B$.$A \cap B \supseteq\{2,3,4\}$ implies that $\{2,3...
GO Classes
641
views
GO Classes
asked
Apr 3
Set Theory & Algebra
goclasses2025_cs_wq4
goclasses
set-theory&algebra
set-theory
power-set
multiple-selects
2-marks
+
–
43
votes
5
answers
166
GATE CSE 2006 | Question: 3
The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false? It is not closed $2$ does not have an inverse $3$ does not have an inverse $8$ does not have an inverse
The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false?It is not closed$2$ does no...
Rucha Shelke
10.0k
views
Rucha Shelke
asked
Sep 16, 2014
Set Theory & Algebra
gatecse-2006
set-theory&algebra
group-theory
normal
+
–
59
votes
7
answers
167
GATE CSE 2006 | Question: 24
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = \min(\pi(B))$, where $\min(S)$ is the smallest integer in the set of integers $S$, and $\pi$(S) is the set of ... $n! \frac{|A ∩ B|}{|A ∪ B|}$ $\dfrac{|A ∩ B|^2}{^n \mathrm{C}_{|A ∪ B|}}$
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = ...
Rucha Shelke
11.4k
views
Rucha Shelke
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2006
set-theory&algebra
normal
set-theory
+
–
14
votes
2
answers
168
GATE CSE 2022 | Question: 40
The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are $\text{TRUE}?$ The chromatic number of the graph is $3.$ The graph has a Hamiltonian path. The following graph is isomorphic to the Peterson ... $3.$ (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
The following simple undirected graph is referred to as the Peterson graph.Which of the following statements is/are $\text{TRUE}?$The chromatic number of the graph is $3....
Arjun
7.7k
views
Arjun
asked
Feb 15, 2022
Graph Theory
gatecse-2022
graph-theory
graph-isomorphism
multiple-selects
2-marks
+
–
35
votes
6
answers
169
GATE CSE 2021 Set 1 | Question: 36
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as: $\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortest path between $u$ and $v$}\}$ Let $M$ be the adjacency matrix of $G$. Define graph $G_2$ ... $\text{diam}(G_2) = \text{diam}(G)$ $\text{diam}(G)< \text{diam}(G_2)\leq 2\; \text{diam}(G)$
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as:$$\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortes...
Arjun
10.1k
views
Arjun
asked
Feb 18, 2021
Graph Theory
gatecse-2021-set1
graph-theory
graph-connectivity
2-marks
+
–
54
votes
5
answers
170
GATE CSE 2001 | Question: 2.2
Consider the following statements: $S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite. $S_2:$ There exists two irrational numbers $x$ and y such that $(x+y)$ ... $S_2$? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Consider the following statements:$S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite.$S_2:$ There exists two irrational numbers $x$ a...
Kathleen
9.1k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
normal
set-theory
+
–
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