The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
Facebook Login
or
Email or Username
Password
Remember
Login
Register

I forgot my password
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Prev
Blogs
New Blog
Exams
Most answered questions in Set Theory & Algebra
Recent
Hot!
Most votes
Most answers
Most views
Featured
Previous GATE
Recent
Hot!
Most votes
Most answers
Most views
Featured
Previous GATE
+59
votes
10
answers
1
GATE2015139
Consider the operations $\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'}$ and $\textit{g (X, Y, Z) = X'YZ + X'YZ' + XY}$ Which one of the following is correct? Both $\left\{\textit{f} \right\}$ and $\left\{ \textit{g}\right\}$ are ... Only $\left\{ \textit{g}\right\}$ is functionally complete Neither $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete
asked
Feb 13, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

8.4k
views
gate20151
settheory&algebra
functions
difficult
+34
votes
10
answers
2
GATE2015240
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
asked
Feb 13, 2015
in
Set Theory & Algebra
by
jothee
Veteran
(
106k
points)

8.3k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+16
votes
8
answers
3
GATE2017147
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
asked
Feb 14, 2017
in
Set Theory & Algebra
by
Arjun
Veteran
(
432k
points)

3.8k
views
gate20171
settheory&algebra
normal
numericalanswers
sets
+55
votes
8
answers
4
GATE2016228
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an odd number ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
asked
Feb 12, 2016
in
Set Theory & Algebra
by
Akash Kanase
Boss
(
41.9k
points)

5.6k
views
gate20162
settheory&algebra
difficult
sets
+2
votes
7
answers
5
is D36 distributive ?
In one text I read that , if n is square free it is DISTRIBUTIVE in other text I read that if n is square free it is BOOLEAN ALGEBRA . Which is most correct ? Here D36 is not square free then... what conclusion can I make ?
asked
Jun 24, 2016
in
Set Theory & Algebra
by
pC
Boss
(
21.5k
points)

1.5k
views
settheory&algebra
lattice
+58
votes
7
answers
6
GATE2016128
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 ___________.
asked
Feb 12, 2016
in
Set Theory & Algebra
by
Sandeep Singh
Loyal
(
7.2k
points)

6.8k
views
gate20161
settheory&algebra
functions
normal
numericalanswers
+28
votes
7
answers
7
GATE200473
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by set containment ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
asked
Sep 19, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

3.2k
views
gate2004
settheory&algebra
partialorder
normal
+25
votes
7
answers
8
GATE200628
A logical binary relation $\odot$ ... $(\sim A\odot B)$ $\sim(A \odot \sim B)$ $\sim(\sim A\odot\sim B)$ $\sim(\sim A\odot B)$
asked
Sep 18, 2014
in
Set Theory & Algebra
by
Rucha Shelke
Active
(
3.3k
points)

1.6k
views
gate2006
settheory&algebra
binaryoperation
+3
votes
6
answers
9
TIFR2019A1
Let $X$ be a set with $n$ elements. How many subsets of $X$ have odd cardinality? $n$ $2^n$ $2^{n/2}$ $2^{n1}$ Can not be determined without knowing whether $n$ is odd or even
asked
Dec 18, 2018
in
Set Theory & Algebra
by
Arjun
Veteran
(
432k
points)

621
views
tifr2019
engineeringmathematics
discretemathematics
settheory&algebra
sets
+33
votes
6
answers
10
GATE2016226
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
asked
Feb 12, 2016
in
Set Theory & Algebra
by
Akash Kanase
Boss
(
41.9k
points)

4.9k
views
gate20162
settheory&algebra
relations
normal
+41
votes
6
answers
11
GATE2015134
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram: For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \wedge y$ are join and meet of $x, y$ ... $p_r = 0$ $p_r = 1$ $0 < p_r ≤ \frac{1}{5}$ $\frac{1}{5} < p_r < 1$
asked
Feb 13, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

5.9k
views
gate20151
settheory&algebra
normal
lattice
+22
votes
6
answers
12
GATE2005IT34
Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the greatest common divisor of $m$ and $n$. $p(q  1)$ $pq$ $\left ( p^{2}1 \right ) (q  1)$ $p(p  1) (q  1)$
asked
Nov 3, 2014
in
Set Theory & Algebra
by
Ishrat Jahan
Boss
(
16.3k
points)

2.1k
views
gate2005it
settheory&algebra
normal
numbertheory
+26
votes
6
answers
13
GATE2005IT33
Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $S_2\subset S_1$. What is the maximum cardinality of C? $n$ $n+1$ $2^{n1} + 1$ $n!$
asked
Nov 3, 2014
in
Set Theory & Algebra
by
Ishrat Jahan
Boss
(
16.3k
points)

3.5k
views
gate2005it
settheory&algebra
normal
sets
+22
votes
6
answers
14
GATE2005IT31
Let $f$ be a function from a set $A$ to a set $B$, $g$ a function from $B$ to $C$, and $h$ a function from $A$ to $C$, such that $h(a) = g(f(a))$ for all $a ∈ A.$ Which of the following statements is always true for all such functions $f$ and $g$? $g$ is ... $h$ is onto $h$ is onto $\implies$ $f$ is onto $h$ is onto $\implies$ $g$ is onto $h$ is onto $\implies$ $f$ and $g$ are onto
asked
Nov 3, 2014
in
Set Theory & Algebra
by
Ishrat Jahan
Boss
(
16.3k
points)

2.6k
views
gate2005it
settheory&algebra
functions
normal
+21
votes
6
answers
15
GATE2007IT23
A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division. $(0, 0) \in P.$ $(a, b) \in P$ if and only if $(a \% 10) \leq (b \% 10$) and $(\frac{a}{10},\frac{b}{10})\in P.$ Consider the ... $P$? (i) and (iii) (ii) and (iv) (i) and (iv) (iii) and (iv)
asked
Oct 30, 2014
in
Set Theory & Algebra
by
Ishrat Jahan
Boss
(
16.3k
points)

2.6k
views
gate2007it
settheory&algebra
partialorder
normal
+15
votes
6
answers
16
GATE19973.1
Let $\left(Z, *\right)$ be an algebraic structure where $Z$ is the set of integers and the operation $*$ is defined by $n*m = \max(n,m)$. Which of the following statements is true for $\left(Z, *\right)$? $\left(Z, *\right)$ is a monoid $\left(Z, *\right)$ is an Abelian group $\left(Z, *\right)$ is a group None of the above
asked
Sep 29, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

2k
views
gate1997
settheory&algebra
grouptheory
normal
+17
votes
6
answers
17
GATE199810a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n3)}{2}$
asked
Sep 26, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

1.3k
views
gate1998
settheory&algebra
descriptive
relations
+26
votes
6
answers
18
GATE200543
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
asked
Sep 21, 2014
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

2.9k
views
gate2005
settheory&algebra
functions
normal
+50
votes
6
answers
19
GATE200625
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left  \left\{j \mid i\in X_j \right\} \right$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
asked
Sep 18, 2014
in
Set Theory & Algebra
by
Rucha Shelke
Active
(
3.3k
points)

3k
views
gate2006
settheory&algebra
normal
functions
+28
votes
5
answers
20
GATE201827
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
asked
Feb 14, 2018
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

5.7k
views
gate2018
settheory&algebra
countableuncountableset
normal
+10
votes
5
answers
21
ISRO20179
The symmetric difference of sets $A=\{1,2, 3,4, 5, 6, 7, 8\}$ and $B= \{1, 3, 5, 6, 7,8,9\}$ is: $\{1, 3, 5, 6, 7,8\}$ $\{2, 4, 9\}$ $\{2, 4\}$ $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$
asked
May 7, 2017
in
Set Theory & Algebra
by
sh!va
Boss
(
33k
points)

3.4k
views
isro2017
settheory&algebra
sets
+24
votes
5
answers
22
GATE2017224
Consider the quadratic equation $x^213x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
asked
Feb 14, 2017
in
Set Theory & Algebra
by
khushtak
Loyal
(
7.1k
points)

4.6k
views
gate20172
polynomials
numericalanswers
settheory&algebra
+33
votes
5
answers
23
GATE2015341
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 $ps=qr$. 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
asked
Feb 15, 2015
in
Set Theory & Algebra
by
jothee
Veteran
(
106k
points)

4.1k
views
gate20153
settheory&algebra
relations
normal
+41
votes
5
answers
24
GATE2015116
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\phi \in 2^{A}$ $\phi \subseteq 2^{A}$ $\left\{5,\left\{6\right\}\right\} \in 2^{A}$ $\left\{5,\left\{6\right\}\right\} \subseteq 2^{A}$ I and III only II and III only I, II and III only I, II and IV only
asked
Feb 13, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

5.6k
views
gate20151
settheory&algebra
sets
normal
+4
votes
5
answers
25
No of surjective functions
The number of surjective functions defined from $A$ to $B$ where A = 5, B = 4, is _______
asked
Dec 22, 2014
in
Set Theory & Algebra
by
dhingrak
Active
(
1k
points)

3.7k
views
settheory&algebra
functions
+24
votes
5
answers
26
GATE19968
Let $F$ be the collection of all functions $f: \{1, 2, 3\} \to \{1, 2, 3\}$. If $f$ and $g \in F$, define an equivalence relation $\sim$ by $f\sim g$ if and only if $f(3) = g(3)$. Find the number of equivalence classes defined by $\sim$. Find the number of elements in each equivalence class.
asked
Oct 10, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

1.9k
views
gate1996
settheory&algebra
relations
functions
normal
descriptive
+17
votes
5
answers
27
GATE19961.1
Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(AB) \cup (BA) \cup (A \cap B)$ is equal to $A \cup B$ $A^c \cup B^c$ $A \cap B$ $A^c \cap B^c$
asked
Oct 9, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

999
views
gate1996
settheory&algebra
easy
sets
+12
votes
5
answers
28
GATE19943.9
Every subset of a countable set is countable. State whether the above statement is true or false with reason.
asked
Oct 6, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

726
views
gate1994
settheory&algebra
normal
sets
descriptive
countableuncountableset
+23
votes
5
answers
29
GATE2014316
Let $\Sigma$ be a finite nonempty alphabet and let $2^{\Sigma^*}$ be the power set of $\Sigma^*$. Which one of the following is TRUE? Both $2^{\Sigma^*}$ and $\Sigma^*$ are countable $2^{\Sigma^*}$ is countable and $\Sigma^*$ is uncountable $2^{\Sigma^*}$ is uncountable and $\Sigma^*$ is countable Both $2^{\Sigma^*}$ and $\Sigma^*$ are uncountable
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
106k
points)

2.8k
views
gate20143
settheory&algebra
sets
normal
countableuncountableset
+50
votes
5
answers
30
GATE2014250
Consider the following relation on subsets of the set $S$ of integers between 1 and 2014. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the following two statements: $S1$ ... $S2$ are true $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
106k
points)

5k
views
gate20142
settheory&algebra
normal
sets
Page:
1
2
3
4
5
6
...
46
next »
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
ISRO CSE 2020 PAPER ANALYSE
BARC OCES/DGFS 2020
ISI CMI PDF by GATE Overflow
Calculus Important Points
Management Trainee Recruitment COAL INDIA 2020
All categories
General Aptitude
1.9k
Engineering Mathematics
7.5k
Discrete Mathematics
5.2k
Mathematical Logic
2.1k
Set Theory & Algebra
1.4k
Combinatory
916
Graph Theory
824
Probability
1k
Linear Algebra
723
Calculus
592
Digital Logic
2.9k
Programming and DS
4.9k
Algorithms
4.4k
Theory of Computation
6.2k
Compiler Design
2.1k
Operating System
4.5k
Databases
4.1k
CO and Architecture
3.4k
Computer Networks
4.2k
Non GATE
1.4k
Others
1.4k
Admissions
595
Exam Queries
573
Tier 1 Placement Questions
23
Job Queries
72
Projects
18
Follow @csegate
Recent Blog Comments
And there is some question like where they...
Yes post order question is also wrong.....
Even the post order question also I think.
SQL for sure, that case 1 case 2 move question...
For how many question can we except that ISRO...
50,737
questions
57,388
answers
198,576
comments
105,414
users