Login
Register
@
Dark Mode
Profile
Edit my Profile
Messages
My favorites
Register
Activity
Q&A
Questions
Unanswered
Tags
Subjects
Users
Ask
Previous Years
Blogs
New Blog
Exams
Dark Mode
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Highest voted questions in Discrete Mathematics
28
votes
6
answers
241
GATE CSE 1995 | Question: 1.19
Let $R$ be a symmetric and transitive relation on a set $A$. Then $R$ is reflexive and hence an equivalence relation $R$ is reflexive and hence a partial order $R$ is reflexive and hence not an equivalence relation None of the above
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
14.3k
views
gate1995
set-theory&algebra
relations
normal
28
votes
3
answers
242
GATE CSE 1993 | Question: 8.6
Let $A$ and $B$ be sets with cardinalities $m$ and $n$ respectively. The number of one-one mappings from $A$ to $B$, when $m < n$, is $m^n$ $^nP_m$ $^mC_n$ $^nC_m$ $^mP_n$
Kathleen
asked
in
Set Theory & Algebra
Sep 29, 2014
by
Kathleen
4.4k
views
gate1993
set-theory&algebra
functions
easy
28
votes
6
answers
243
GATE CSE 2014 Set 2 | Question: 53
Which one of the following Boolean expressions is NOT a tautology? $((\,a\,\to\,b\,)\,\wedge\,(\,b\,\to\,c))\,\to\,(\,a\,\to\,c)$ $(\,a\,\to\,c\,)\,\to\,(\,\sim b\,\to\,(a\,\wedge\,c))$ $(\,a\,\wedge\,b\,\wedge\,c)\,\to\,(\,c\vee\,a)$ $a\,\to\,(b\,\to\,a)$
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
9.1k
views
gatecse-2014-set2
mathematical-logic
propositional-logic
normal
28
votes
7
answers
244
GATE CSE 2009 | Question: 26
Consider the following well-formed formulae: $\neg \forall x(P(x))$ $\neg \exists x(P(x))$ $\neg \exists x(\neg P(x))$ $\exists x(\neg P(x))$ Which of the above are equivalent? $\text{I}$ and $\text{III}$ $\text{I}$ and $\text{IV}$ $\text{II}$ and $\text{III}$ $\text{II}$ and $\text{IV}$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
5.5k
views
gatecse-2009
mathematical-logic
normal
first-order-logic
28
votes
3
answers
245
GATE CSE 2000 | Question: 4
Let $S= \{0, 1, 2, 3, 4, 5, 6, 7\}$ and $⊗$ denote multiplication modulo $8,$ that is, $x ⊗ y= (xy) \mod 8$ Prove that $( \{ 0, 1\}, ⊗)$ is not a group. Write three distinct groups $(G, ⊗)$ where $G ⊂ S$ and $G$ has $2$ elements.
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
4.1k
views
gatecse-2000
set-theory&algebra
descriptive
group-theory
28
votes
8
answers
246
GATE CSE 2008 | Question: 2
If $P, Q, R$ are subsets of the universal set U, then $(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$ is $Q^c \cup R^c$ $P \cup Q^c \cup R^c$ $P^c \cup Q^c \cup R^c$ U
Kathleen
asked
in
Set Theory & Algebra
Sep 11, 2014
by
Kathleen
9.3k
views
gatecse-2008
normal
set-theory&algebra
set-theory
27
votes
3
answers
247
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 12
Two compound propositions are logically equivalent if they have the same truth table. For example, the following two compound propositions are logically equivalent: $\mathrm{p} \rightarrow \mathrm{q}$ ... propositional variables, how many compound propositions are there that are Not logically equivalent to each other?
GO Classes
asked
in
Mathematical Logic
Mar 26, 2023
by
GO Classes
1.0k
views
goclasses2024_wq5
numerical-answers
goclasses
mathematical-logic
propositional-logic
2-marks
27
votes
9
answers
248
GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$
Arjun
asked
in
Mathematical Logic
Feb 18, 2021
by
Arjun
8.7k
views
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
27
votes
5
answers
249
GATE CSE 2021 Set 1 | Question: 43
A relation $R$ is said to be circular if $a\text{R}b$ and $b\text{R}c$ together imply $c\text{R}a$. Which of the following options is/are correct? If a relation $S$ is reflexive and symmetric, then $S$ is an equivalence relation ... and circular, then $S$ is an equivalence relation. If a relation $S$ is transitive and circular, then $S$ is an equivalence relation.
Arjun
asked
in
Set Theory & Algebra
Feb 18, 2021
by
Arjun
8.1k
views
gatecse-2021-set1
multiple-selects
set-theory&algebra
relations
2-marks
27
votes
2
answers
250
GATE CSE 1990 | Question: 3-xi
A graph is planar if and only if, It does not contain a subgraph homeomorphic to $k_{5}$ and $k_{3, 3}$. It does not contain a subgraph isomorphic to $k_{5}$ and $k_{3, 3}$. It does not contain a subgraph isomorphic to $k_{5}$ or $k_{3, 3}$ It does not contain a subgraph homeomorphic to $k_{5}$ or $k_{3, 3}$.
makhdoom ghaya
asked
in
Graph Theory
Nov 23, 2016
by
makhdoom ghaya
12.6k
views
gate1990
normal
graph-theory
graph-planarity
multiple-selects
27
votes
5
answers
251
TIFR CSE 2014 | Part A | Question: 8
All that glitters is gold. No gold is silver. Claims: No silver glitters. Some gold glitters. Then, which of the following is TRUE? Only claim $1$ follows. Only claim $2$ follows. Either claim $1$ or claim $2$ follows but not both. Neither claim $1$ nor claim $2$ follows. Both claim $1$ and claim $2$ follow.
makhdoom ghaya
asked
in
Mathematical Logic
Nov 9, 2015
by
makhdoom ghaya
3.5k
views
tifr2014
mathematical-logic
first-order-logic
27
votes
4
answers
252
GATE IT 2006 | Question: 23
Let $P$, $Q$ and $R$ be sets let Δ denote the symmetric difference operator defined as $PΔQ=(P \cup Q) - (P ∩ Q).$ Using Venn diagrams, determine which of the following is/are TRUE? $PΔ (Q ∩ R) = (P Δ Q) ∩ (P Δ R)$ $P ∩ (Q ∩ R) = (P ∩ Q) Δ (P Δ R)$ I only II only Neither I nor II Both I and II
Ishrat Jahan
asked
in
Set Theory & Algebra
Oct 31, 2014
by
Ishrat Jahan
5.7k
views
gateit-2006
set-theory&algebra
normal
set-theory
27
votes
5
answers
253
GATE CSE 1995 | Question: 21
Let $G_1$ and $G_2$ be subgroups of a group $G$. Show that $G_1 \cap G_2$ is also a subgroup of $G$. Is $G_1 \cup G_2$ always a subgroup of $G$?.
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
6.5k
views
gate1995
set-theory&algebra
group-theory
normal
descriptive
proof
27
votes
4
answers
254
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
9.9k
views
gate1995
set-theory&algebra
group-theory
27
votes
3
answers
255
GATE CSE 1993 | Question: 8.4
Let A be a finite set of size n. The number of elements in the power set of $A\times A$ is: $2^{2^n}$ $2^{n^2}$ $\left(2^n\right)^2$ $\left(2^2\right)^n$ None of the above
Kathleen
asked
in
Set Theory & Algebra
Sep 29, 2014
by
Kathleen
6.9k
views
gate1993
set-theory&algebra
easy
set-theory
27
votes
4
answers
256
GATE CSE 1997 | Question: 4.4
A polynomial $p(x)$ is such that $p(0) = 5, p(1) = 4, p(2) = 9$ and $p(3) = 20$. The minimum degree it should have is $1$ $2$ $3$ $4$
Kathleen
asked
in
Set Theory & Algebra
Sep 29, 2014
by
Kathleen
6.8k
views
gate1997
set-theory&algebra
normal
polynomials
27
votes
8
answers
257
GATE CSE 2005 | Question: 50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
gatecse
asked
in
Combinatory
Sep 21, 2014
by
gatecse
8.2k
views
gatecse-2005
normal
generating-functions
27
votes
4
answers
258
GATE CSE 2009 | Question: 1
Which one of the following is NOT necessarily a property of a Group? Commutativity Associativity Existence of inverse for every element Existence of identity
gatecse
asked
in
Set Theory & Algebra
Sep 15, 2014
by
gatecse
8.1k
views
gatecse-2009
set-theory&algebra
easy
group-theory
26
votes
6
answers
259
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Arjun
asked
in
Combinatory
Feb 15, 2022
by
Arjun
9.4k
views
gatecse-2022
combinatory
generating-functions
2-marks
26
votes
4
answers
260
TIFR CSE 2017 | Part A | Question: 11
Let $f \: \circ \: g$ denote function composition such that $(f \circ g)(x) = f(g(x))$. Let $f: A \rightarrow B$ such that for all $g \: : \: B \rightarrow A$ and $h \: : \: B \rightarrow A$ ... ) $f$ is one-to-one (injective) $f$ is both one-to-one and onto (bijective) the range of $f$ is finite the domain of $f$ is finite
go_editor
asked
in
Set Theory & Algebra
Dec 22, 2016
by
go_editor
4.0k
views
tifr2017
set-theory&algebra
functions
Page:
« prev
1
...
8
9
10
11
12
13
14
15
16
17
18
...
355
next »
Subscribe to GATE CSE 2024 Test Series
Subscribe to GO Classes for GATE CSE 2024
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
-tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Post GATE 2024 Guidance [Counseling tips and resources]
GATE CSE 2024 Result Responses
[Project Contest] Pytorch backend support for MLCommons Cpp Inference implementation
Participating in MLCommons Inference v4.0 submission (deadline is February 23 12pm IST)
IIITH PGEE 2024 Test Series by GO Classes
Subjects
All categories
General Aptitude
(3.5k)
Engineering Mathematics
(10.4k)
Discrete Mathematics
(7.1k)
Mathematical Logic
(2.5k)
Set Theory & Algebra
(1.9k)
Combinatory
(1.6k)
Graph Theory
(1.1k)
Probability
(1.4k)
Linear Algebra
(1.1k)
Calculus
(792)
Optimization
(0)
Digital Logic
(3.6k)
Programming and DS
(6.2k)
Algorithms
(4.8k)
Theory of Computation
(6.9k)
Compiler Design
(2.5k)
Operating System
(5.2k)
Databases
(4.8k)
CO and Architecture
(4.0k)
Computer Networks
(4.9k)
Artificial Intelligence
(79)
Machine Learning
(48)
Data Mining and Warehousing
(25)
Non GATE
(1.4k)
Others
(2.7k)
Admissions
(684)
Exam Queries
(1.6k)
Tier 1 Placement Questions
(17)
Job Queries
(80)
Projects
(11)
Unknown Category
(870)
64.3k
questions
77.9k
answers
244k
comments
80.0k
users
Recent Blog Comments
category ?
Hi @Arjun sir, I have obtained a score of 591 in ...
download here
Can you please tell about IIT-H mtech CSE self...
Please add your admission queries here:...
Network Sites
GO Mechanical
GO Electrical
GO Electronics
GO Civil
CSE Doubts
Aptitude Overflow