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+6
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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
(
59.2k
points)

42.2k
views
relations
+19
votes
2
answers
2
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
+32
votes
4
answers
3
GATE19976.3
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
asked
Sep 29, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

8.4k
views
gate1997
settheory&algebra
relations
normal
+59
votes
10
answers
4
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
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
+2
votes
1
answer
6
Let a relation R be defined on the set of all real numbers by a R b <=> 1 + ab > 0 thus R is ?
asked
Nov 2, 2017
in
Set Theory & Algebra
by
techbrk3
(
409
points)

6.9k
views
+58
votes
7
answers
7
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
+24
votes
5
answers
8
GATE20057
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
asked
Sep 22, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

6.6k
views
gate2005
settheory&algebra
normal
relations
+4
votes
2
answers
9
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
+26
votes
4
answers
10
GATE200721
How many different nonisomorphic Abelian groups of order $4$ are there? $2$ $3$ $4$ $5$
asked
Sep 22, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

6.1k
views
gate2007
grouptheory
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)

5.8k
views
gate20151
settheory&algebra
normal
lattice
+27
votes
5
answers
12
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
+55
votes
8
answers
13
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
+41
votes
5
answers
14
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
+4
votes
1
answer
15
equivalence relaton
How many different equivalence relations with exactly three equivalence classes are there on a set with 5 elements 10 15 25 30
asked
Dec 9, 2016
in
Set Theory & Algebra
by
Sanjay Sharma
Boss
(
49.3k
points)

5.3k
views
relations
+44
votes
4
answers
16
GATE2014350
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

5.3k
views
gate20143
settheory&algebra
grouptheory
numericalanswers
normal
+50
votes
3
answers
17
GATE2014349
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$ ... the following is CORRECT? $P, Q$ and $R$ are true Only $Q$ and $R$ are true Only $P$ and $Q$ are true Only $R$ is true
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

5.2k
views
gate20143
settheory&algebra
functions
normal
+50
votes
5
answers
18
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
(
105k
points)

5k
views
gate20142
settheory&algebra
normal
sets
+33
votes
6
answers
19
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
+24
votes
5
answers
20
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
+39
votes
4
answers
21
GATE201432
Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE? For any subsets $A$ and $B$ of $X, fA \cup B = f(A) + f(B)$ For any subsets $A$ and $B$ of $X, f(A \cap B) = f(A) \cap f(B)$ For any subsets $A$ and $B$ ... $S$ and $T$ of $Y, f^{1}(S \cap T) = f^{1}(S) \cap f^{1}(T)$
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

4.5k
views
gate20143
settheory&algebra
functions
normal
+43
votes
5
answers
22
GATE2014150
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

4.4k
views
gate20141
settheory&algebra
functions
permutationandcombination
numericalanswers
+38
votes
5
answers
23
GATE20002.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
asked
Sep 14, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

4.3k
views
gate2000
settheory&algebra
easy
sets
+25
votes
4
answers
24
GATE2017221
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
asked
Feb 14, 2017
in
Set Theory & Algebra
by
khushtak
Loyal
(
7.1k
points)

4.1k
views
gate20172
settheory&algebra
lattice
numericalanswers
normal
+27
votes
1
answer
25
GATE200726
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:
asked
Sep 22, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

4.1k
views
gate2007
settheory&algebra
normal
partialorder
descriptive
+33
votes
5
answers
26
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
(
105k
points)

4.1k
views
gate20153
settheory&algebra
relations
normal
+13
votes
4
answers
27
GATE201819
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
asked
Feb 14, 2018
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

3.9k
views
gate2018
grouptheory
numericalanswers
settheory&algebra
+32
votes
3
answers
28
GATE2015323
Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $T$ denote the number of elements in $T$ and $T'$ denote the complement of $T$. For any $T, R \in U \text{ let } T \backslash R$ be the set of all elements in $T$ which ... $X \backslash Y = \phi)$ $\forall X \in U, \forall Y \in U, (X \backslash Y = Y' \backslash X')$
asked
Feb 14, 2015
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

3.9k
views
gate20153
settheory&algebra
sets
normal
+16
votes
8
answers
29
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
(
431k
points)

3.8k
views
gate20171
settheory&algebra
normal
numericalanswers
sets
+23
votes
4
answers
30
GATE2008IT28
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only
asked
Oct 28, 2014
in
Set Theory & Algebra
by
Ishrat Jahan
Boss
(
16.3k
points)

3.8k
views
gate2008it
settheory&algebra
lattice
normal
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