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Hot questions in Discrete Mathematics
45
votes
4
answers
161
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
+
–
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
2.4k
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
9.8k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
normal
set-theory
group-theory
+
–
60
votes
7
answers
165
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
+
–
13
votes
1
answer
166
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
670
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
167
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
10.1k
views
Rucha Shelke
asked
Sep 16, 2014
Set Theory & Algebra
gatecse-2006
set-theory&algebra
group-theory
normal
+
–
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:$$\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortes...
Arjun
10.2k
views
Arjun
asked
Feb 18, 2021
Graph Theory
gatecse-2021-set1
graph-theory
graph-connectivity
2-marks
+
–
54
votes
5
answers
170
GATE CSE 2001 | Question: 2.2
Consider the following statements: $S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite. $S_2:$ There exists two irrational numbers $x$ and y such that $(x+y)$ ... $S_2$? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Consider the following statements:$S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite.$S_2:$ There exists two irrational numbers $x$ a...
Kathleen
9.1k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
normal
set-theory
+
–
15
votes
3
answers
171
GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 10
Given the truth table of a Binary Operation \$ as follows: $ ... }$ Identify the matching Boolean Expression. $X \$ \neg Y$ $\neg X \$ Y$ $\neg X \$ \neg Y$ none of the options
Given the truth table of a Binary Operation \$ as follows:$$\begin{array}{|l|l|l|l|} \hline {} \text{X} & \text{Y }& \text{X\$Y }\\ \hline \text{1} & \text{0 }& ...
GO Classes
1.3k
views
GO Classes
asked
Dec 5, 2022
Mathematical Logic
goclasses2025_cs_wq1
goclasses
mathematical-logic
propositional-logic
2-marks
+
–
8
votes
1
answer
172
GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 8
Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is listed in lexicographic order, then the next element after $((1,0), c,(1,1))$ is $((1,0), a,(0,0))$ $((1,1), c,(0,0))$ $((1,1), a,(0,0))$ $((1,1), a,(1,1))$
Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is...
GO Classes
175
views
GO Classes
asked
Apr 10
Set Theory & Algebra
goclasses2025_cs_wq5
goclasses
discrete-mathematics
set-theory&algebra
set-theory
2-marks
+
–
4
votes
1
answer
173
GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 9
Which of the following statements is $\textbf{TRUE}$? For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=A-(B \cup C)$. For all sets $A, B$, and $C$, if $A \cap C=B \cap C$ then $A=B$.
Which of the following statements is $\textbf{TRUE}$?For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$.For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$.For all sets ...
GO Classes
149
views
GO Classes
asked
Apr 10
Set Theory & Algebra
goclasses2025_cs_wq5
goclasses
discrete-mathematics
set-theory&algebra
set-theory
2-marks
+
–
31
votes
5
answers
174
GATE CSE 1989 | Question: 14a
Symbolize the expression "Every mother loves her children" in predicate logic.
Symbolize the expression "Every mother loves her children" in predicate logic.
makhdoom ghaya
6.1k
views
makhdoom ghaya
asked
Dec 15, 2016
Mathematical Logic
gate1989
descriptive
first-order-logic
mathematical-logic
+
–
54
votes
6
answers
175
GATE CSE 2006 | Question: 26
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened. ...
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or ...
Rucha Shelke
9.4k
views
Rucha Shelke
asked
Sep 18, 2014
Mathematical Logic
gatecse-2006
mathematical-logic
normal
first-order-logic
+
–
41
votes
5
answers
176
GATE CSE 2012 | Question: 37
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set? $ 2^{n}$ $2^{n} – 1$ $2^{n} – 2$ $2(2^{n} – 2)$
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set?$ 2^{n}$$2^{n} – 1$$2^{n} – 2$$2(2^{n} – 2)$
gatecse
9.5k
views
gatecse
asked
Sep 26, 2014
Set Theory & Algebra
gatecse-2012
set-theory&algebra
functions
normal
+
–
11
votes
1
answer
177
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 $\mathrm{R}$ ... $\forall x \in P . \exists y \in P . x R y$
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-ord...
GO Classes
716
views
GO Classes
asked
Jan 21
Mathematical Logic
goclasses2024-mockgate-12
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
+
–
7
votes
1
answer
178
GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 9
Which of the following statements is /are TRUE? $2 \in A \cup B$ implies that if $2 \notin A$ then $2 \in B$. $\{2,3\} \subseteq A$ implies that $2 \in A$ and $3 \in A$. $A \cap B \supseteq\{2,3\}$ ... $A-B \supseteq\{3\}$ and $\{2\} \subseteq B$ implies that $\{2,3\} \subseteq A \cup B$.
Which of the following statements is /are TRUE?$2 \in A \cup B$ implies that if $2 \notin A$ then $2 \in B$.$\{2,3\} \subseteq A$ implies that $2 \in A$ and $3 \in A$.$A ...
GO Classes
173
views
GO Classes
asked
Apr 3
Set Theory & Algebra
goclasses2025_cs_wq4
goclasses
set-theory&algebra
set-theory
multiple-selects
2-marks
+
–
0
votes
1
answer
179
Discrete Mathematics | Set Theory | Relation | Equivalance Relation
which if the following statement is True for every set? a. $\exists$ a equivalence class that is also a partition set. b. Every equivalence relation on a set defines a partition of that set. c. $\exists$ a partition of a set that is also equal to equivalence class of the set on some equivalence relation.
which if the following statement is True for every set?a. $\exists$ a equivalence class that is also a partition set.b. Every equivalence relation on a set defines a part...
RahulVerma3
103
views
RahulVerma3
asked
Apr 12
Set Theory & Algebra
discrete-mathematics
set-theory
analytical-aptitude
equivalence-class
+
–
1
votes
2
answers
180
Permutation and combination
Your mother-in-law buys 1000 small gifts to give to relatives for Christmas. Each of the 1000 things in different. There are 25 relatives to give gifts to. How many ways are there to distribute the gifts? The correct answer is $25^{1000}$. I ... ? I know some people may feel its silly question but please trust me many people like me are confused with this doubt.
Your mother-in-law buys 1000 small gifts to give to relatives for Christmas. Each of the 1000 things in different. There are 25 relatives to give gifts to. How many ways ...
rajishu07
150
views
rajishu07
asked
Apr 2
Mathematical Logic
combinatory
engineering-mathematics
+
–
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