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Previous GATE
+6
votes
1
answer
1
relation
Number of relations $S$ over set $\{0,1,2,3 \}$ such that $(x,y) \in S \Rightarrow x = y$
asked
Dec 27, 2017
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Veteran
(
59k
points)

42.2k
views
relations
+58
votes
10
answers
2
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)

8.3k
views
gate20151
settheory&algebra
functions
difficult
+55
votes
8
answers
3
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)

5.5k
views
gate20162
settheory&algebra
difficult
sets
+27
votes
5
answers
4
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)

5.6k
views
gate2018
settheory&algebra
countableuncountableset
normal
+34
votes
10
answers
5
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
(
105k
points)

8.2k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+41
votes
6
answers
6
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)

5.8k
views
gate20151
settheory&algebra
normal
lattice
+40
votes
5
answers
7
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)

5.5k
views
gate20151
settheory&algebra
sets
normal
+33
votes
6
answers
8
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)

4.8k
views
gate20162
settheory&algebra
relations
normal
+19
votes
2
answers
9
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?
asked
Oct 24, 2014
in
Set Theory & Algebra
by
shree
Active
(
3.5k
points)

13.9k
views
settheory&algebra
+58
votes
6
answers
10
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)

6.7k
views
gate20161
settheory&algebra
functions
normal
numericalanswers
+10
votes
2
answers
11
ISRODEC20172
Consider the set of integers $I.$ Let $D$ denote "divides with an integer quotient" (e.g. $4D8$ but not $4D7$). Then $D$ is Reflexive, Not Symmetric, Transitive Not Reflexive, Not Antisymmetric, Transitive Reflexive, Antisymmetric, Transitive Not Reflexive, Not Antisymmetric, Not Transitive
asked
Dec 17, 2017
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

2.6k
views
isrodec2017
settheory&algebra
relations
+50
votes
6
answers
12
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
+11
votes
3
answers
13
GATE201910
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{1}$ Which of the above is/are equivalence relation/relations? $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
asked
Feb 7, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

3.5k
views
gate2019
engineeringmathematics
discretemathematics
settheory&algebra
grouptheory
+1
vote
1
answer
14
ISRO202076
If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$ Then $(A \cup B’) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ \ \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$
asked
Jan 13
in
Set Theory & Algebra
by
Satbir
Boss
(
24k
points)

136
views
isro2020
discretemathematics
settheory&algebra
sets
easy
0
votes
1
answer
15
$\textbf{NTA NET DEC 2019 (group)}$
Consider the following statements: $\mathbf{S_1:}\;\;$If a group $\mathbf{(G,*)}$ is of order $\mathbf n$ and $\mathrm {a \in G}$ is such that $\mathrm {a^n=e}$ for some integer $\mathrm {m \le n}$ then $\mathbf m$ must divide $\mathbf n$ ... $(3)\;\;\;\text{Niether}\; \mathrm{S_1}\;\text{nor}\;\mathrm{S_2}$
asked
Dec 29, 2019
in
Set Theory & Algebra
by
Sanjay Sharma
Boss
(
49.3k
points)

98
views
ugcnetdec2019ii
grouptheory
+7
votes
3
answers
16
UGCNETJune2019II1
Consider the poset $( \{3,5,9,15,24,45 \}, \mid).$ Which of the following is correct for the given poset ? There exist a greatest element and a least element There exist a greatest element but not a least element There exist a least element but not a greatest element There does not exist a greatest element and a least element
asked
Jul 2, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

785
views
ugcnetjune2019ii
poset
settheory&algebra
+26
votes
6
answers
17
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
+34
votes
3
answers
18
GATE200331
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\implies\) P(y) for all $x, y \in S$ satisfying $x \leq y$ ... False for all x \(\in\) S such that b ≤ x and x ≠ c P(x) = False for all x \(\in\) S such that a ≤ x and b ≤ x
asked
Sep 16, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

3.3k
views
gate2003
settheory&algebra
partialorder
normal
propositionallogic
0
votes
2
answers
19
Hasse Doubt
what is the least upper bound of {a, b, c}?
asked
May 23, 2019
in
Set Theory & Algebra
by
aditi19
Active
(
5.2k
points)

132
views
hassediagram
settheory&algebra
lattice
partialorder
+2
votes
1
answer
20
GO2019FLT111
Which one of the following best expresses the generating function sequence $\{a_n\}$, for the given closed form representation? $F(x) = \frac{1}{1xx^2}$ $a_n=a_{n1}+3, n>0, a_0=1$ $a_n=a_{n1}+a_{n2}, n>1, a_0=1, a_1=1$ $a_n=2n+3, n>1$ $a_n=2a_{n1}+3, n>1, a_0=1$
asked
Dec 27, 2018
in
Set Theory & Algebra
by
Ruturaj Mohanty
Active
(
2.7k
points)

315
views
go2019flt1
generatingfunctions
settheory&algebra
+1
vote
2
answers
21
ISI2018DCG7
You are given three sets $A,B,C$ in such a way that the set $B \cap C$ consists of $8$ elements, the set $A\cap B$ consists of $7$ elements, and the set $C\cap A$ consists of $7$ elements. The minimum number of elements in the set $A\cup B\cup C$ is $8$ $14$ $15$ $22$
asked
Sep 18, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

49
views
isi2018dcg
sets
+29
votes
4
answers
22
GATE2015254
Let $X$ and $Y$ denote the sets containing 2 and 20 distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being onetoone is ______.
asked
Feb 13, 2015
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

2.8k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+4
votes
2
answers
23
How many transitive relations are there on a set with n elements if a)n=1 b) n=2 c) n=3
asked
Mar 7, 2017
in
Set Theory & Algebra
by
Sanjay Sharma
Boss
(
49.3k
points)

6.2k
views
+34
votes
5
answers
24
GATE200624
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 integers obtained by applying ... $n! \frac{A ∩ B}{A ∪ B}$ $\dfrac{A ∩ B^2}{^n \mathrm{C}_{A ∪ B}}$
asked
Sep 18, 2014
in
Set Theory & Algebra
by
Rucha Shelke
Active
(
3.3k
points)

3.3k
views
gate2006
settheory&algebra
normal
sets
+1
vote
2
answers
25
ISI2015MMA7
Let $X$ be the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$. Define the set $\mathcal{R}$ by $\mathcal{R} = \{(x,y) \in X \times X : x$ and $y$ have the same remainder when divided by $3\}$. Then the number of elements in $\mathcal{R}$ is $40$ $36$ $34$ $33$
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

33
views
isi2015mma
sets
cartesianproduct
+5
votes
2
answers
26
GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
asked
Jun 6, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

413
views
gate1995
settheory&algebra
numericalanswers
sets
+1
vote
1
answer
27
ISI2018DCG5
Let $A$ be the set of all prime numbers, $B$ be the set of all even prime numbers, and $C$ be the set of all odd prime numbers. Consider the following three statements in this regard: $A=B\cup C$. $B$ ... statements is true. Exactly one of the above statements is true. Exactly two of the above statements are true. All the above three statements are true.
asked
Sep 18, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

30
views
isi2018dcg
sets
+2
votes
1
answer
28
ISI2014DCG15
Let $\mathbb{N}=\{1,2,3, \dots\}$ be the set of natural numbers. For each $n \in \mathbb{N}$, define $A_n=\{(n+1)k, \: k \in \mathbb{N} \}$. Then $A_1 \cap A_2$ equals $A_3$ $A_4$ $A_5$ $A_6$
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

50
views
isi2014dcg
sets
algebra
+1
vote
2
answers
29
ISI2015MMA5
A set contains $2n+1$ elements. The number of subsets of the set which contain at most $n$ elements is $2^n$ $2^{n+1}$ $2^{n1}$ $2^{2n}$
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

49
views
isi2015mma
sets
subsets
+1
vote
1
answer
30
ISI2014DCG35
Let $A$ and $B$ be disjoint sets containing $m$ and $n$ elements respectively, and let $C=A \cup B$. Then the number of subsets $S$ (of $C$) which contains $p$ elements and also has the property that $S \cap A$ contains $q$ ... $\begin{pmatrix} m \\ pq \end{pmatrix} \times \begin{pmatrix} n \\ q \end{pmatrix}$
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

37
views
isi2014dcg
sets
disjointsets
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