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Recent questions and answers in Set Theory & Algebra
+20
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4
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1
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.
answered
5 days
ago
in
Set Theory & Algebra
by
Debargha Bhattacharj
Junior
(
597
points)

1.6k
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gate1996
settheory&algebra
relations
functions
normal
descriptive
+1
vote
1
answer
2
REGARDING DISCRETE MATHS SYLLABUS
FIELD AND RING ARE IN SYLLABUS???
answered
6 days
ago
in
Set Theory & Algebra
by
Arjun
Veteran
(
418k
points)

76
views
+2
votes
2
answers
3
UGCNETDec2012II4
The power set of the set $\{ \Phi \}$ is $\{ \Phi \}$ $\{ \Phi, \{ \Phi \} \}$ $\{ 0 \}$ $\{ 0, \Phi , \{ \Phi \} \}$
answered
6 days
ago
in
Set Theory & Algebra
by
omsanchitjain
(
33
points)

474
views
ugcnetdec2012ii
settheory&algebra
sets
powerset
+2
votes
3
answers
4
UGCNETDec2015II3
Which of the following is/are not true ? The set of negative integers is countable. The set of integers that are multiples of 7 is countable. The set of even integers is countable. The set of real numbers between 0 and 1⁄2 is countable. a and c b and d b only d only
answered
6 days
ago
in
Set Theory & Algebra
by
omsanchitjain
(
33
points)

707
views
ugcnetdec2015ii
discretemathematics
settheory
+2
votes
1
answer
5
Countable and Uncountable Self Doubt 2
Which of the following is always correct? A. Cross product of two countable set is countable B. Cross product of two countable set is uncountable C. Cross product of two uncountable set is countable D. Cross product of uncountable ... E. Cross product of uncountable and countable set is countable F. Cross product of uncountable and countable set is uncountable
answered
Sep 5
in
Set Theory & Algebra
by
Sandee
(
11
points)

91
views
theoryofcomputation
countableuncountableset
settheory&algebra
0
votes
1
answer
6
Hasse Doubt
what is the least upper bound of {a, b, c}?
answered
Sep 4
in
Set Theory & Algebra
by
bhupendrakumar
(
39
points)

65
views
hassediagram
settheory&algebra
lattice
partialorder
+3
votes
3
answers
7
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
answered
Sep 4
in
Set Theory & Algebra
by
bhupendrakumar
(
39
points)

330
views
ugcnetjune2019ii
poset
settheory&algebra
+1
vote
2
answers
8
isro exam december 2017
The number of elements in the power set of {{1,2},{2,1,1},{2,1,1,2}} is:
answered
Sep 1
in
Set Theory & Algebra
by
GoalSet1
(
163
points)

533
views
isro2017
+43
votes
4
answers
9
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: $3m$ $3n$ $2m+1$ $2n+1$
answered
Aug 27
in
Set Theory & Algebra
by
JashanArora
(
313
points)

2.4k
views
gate2006
settheory&algebra
normal
functions
+29
votes
4
answers
10
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 ... $n! \frac{A ∩ B}{A ∪ B}$ $\dfrac{A ∩ B^2}{^n \mathrm{C}_{A ∪ B}}$
answered
Aug 27
in
Set Theory & Algebra
by
JashanArora
(
313
points)

2.7k
views
gate2006
settheory&algebra
normal
sets
+28
votes
10
answers
11
GATE2015240
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
answered
Aug 26
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
46.5k
points)

7.5k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+4
votes
5
answers
12
No of surjective functions
The number of surjective functions defined from $A$ to $B$ where A = 5, B = 4, is _______
answered
Aug 26
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
46.5k
points)

3.5k
views
settheory&algebra
functions
+4
votes
2
answers
13
TIFR2010MathsA5
Let $f$ be an one to one function from the closed interval [0, 1] to the set of real numbers $R$, then. $f$ must be onto. Range of $f$ must contain a rational number. Range of $f$ must contain an irrational number. Range of $f$ must contain both rational and irrational numbers.
answered
Aug 23
in
Set Theory & Algebra
by
Himanshijoshi31
(
11
points)

739
views
tifrmaths2010
settheory&algebra
functions
+18
votes
5
answers
14
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 $n$. $p(q  1)$ $pq$ $\left ( p^{2}1 \right ) (q  1)$ $p(p  1) (q  1)$
answered
Aug 22
in
Set Theory & Algebra
by
MRINMOY_HALDER
Active
(
2.1k
points)

1.7k
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gate2005it
settheory&algebra
normal
numbertheory
+22
votes
3
answers
15
GATE20002.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having 1 equivalence class $R$ is an equivalence relation having 2 equivalence classes $R$ is an equivalence relation having 3 equivalence classes
answered
Aug 21
in
Set Theory & Algebra
by
MRINMOY_HALDER
Active
(
2.1k
points)

2.7k
views
gate2000
settheory&algebra
relations
normal
+1
vote
1
answer
16
set theory
answered
Aug 19
in
Set Theory & Algebra
by
Debadrita Talapatra
(
11
points)

48
views
settheory&algebra
discretemathematics
engineeringmathematics
sets
+25
votes
4
answers
17
GATE200922
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators
answered
Aug 9
in
Set Theory & Algebra
by
spike500
(
29
points)

1.8k
views
gate2009
settheory&algebra
normal
groups
0
votes
1
answer
18
Kenneth Rosen Edition 7th Exercise 2.3 Question 27 (Page No. 153)
Prove that a strictly decreasing function from $R$ to itself is onetoone. Give an example of an decreasing function from $R$ to itself that is not onetoone
answered
Jul 17
in
Set Theory & Algebra
by
chirudeepnamini
Junior
(
967
points)

11
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
1
answer
19
Kenneth Rosen Edition 7th Exercise 2.2 Question 32 (Page No. 137)
Find the symmetric difference of $\left \{ 1,3,5 \right \}$ and $\left \{ 1,2,3 \right \}.$
answered
Jul 12
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
46.5k
points)

16
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
1
answer
20
Kenneth Rosen Edition 7th Exercise 2.2 Question 35 (Page No. 137)
Show that $A\oplus B = (A \cup B) – (A \cap B).$
answered
Jul 12
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
46.5k
points)

8
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
1
answer
21
Kenneth Rosen Edition 7th Exercise 2.2 Question 36 (Page No. 137)
Show that $A \oplus B = (AB) \cup (BA).$
answered
Jul 12
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
46.5k
points)

6
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
2
answers
22
Kenneth Rosen Edition 7th Exercise 2.2 Question 37 (Page No. 137)
Show that if $A$ is a subset of a universal set $U$, then $A \oplus A = \phi.$ $A \oplus \phi = A.$ $A \oplus U = \sim A.$ $A \oplus \sim A= U.$
answered
Jul 11
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
46.5k
points)

39
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
2
answers
23
Kenneth Rosen Edition 7th Exercise 2.3 Question 69 (Page No. 155)
Find the inverse function of $f(x) = x^3 +1.$
answered
Jul 11
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
46.5k
points)

41
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
24
Kenneth Rosen Edition 6th Exercise 7.5 Question 3 e (Page No. 507)
Which of these relations on the set of all functions from Z to Z are equivalence relations? Determine the properties of an equivalence relation that the others lack. {(f, g)  f(0) = g(1) and f(1) = g(0)} In many ... made to check the reflexive property. Why can't we check f(0)=f(0) to confirm the reflexive property. Please help.
answered
Jul 5
in
Set Theory & Algebra
by
srestha
Veteran
(
114k
points)

71
views
discretemathematics
kennethrosen
+1
vote
1
answer
25
UGCNETJune2019II13
How many different Boolean functions of degree $n$ are the $2^{2^n}$ $(2^2)^n$ $2^{2^n} 1$ $2^n$
answered
Jul 3
in
Set Theory & Algebra
by
Satbir
Boss
(
18k
points)

69
views
ugcnetjune2019ii
boolean
function
+1
vote
2
answers
26
UGCNETJune2019II9
Find the zeroone matrix of the transitive closure of the relation given by the matrix $A$ : $A =\begin{bmatrix} 1 & 0& 1\\ 0 & 1 & 0\\ 1& 1& 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 1& 1\\ 0 & 1 & 0\\ 1& 0& 1 \end{bmatrix}$
answered
Jul 3
in
Set Theory & Algebra
by
Ram Swaroop
Active
(
4k
points)

107
views
ugcnetjune2019ii
settheory&algebra
+1
vote
1
answer
27
Kenneth Rosen Edition 7th Exercise 2.1 Question 23 (Page No. 126)
How many elements does each of these sets have where $a$ and $b$ are distinct elements? $P (\left \{a,b, \left \{a,b \right \} \right \})$ $P\left \{ \phi, a, \left \{ a \right \},\left \{ \left \{ a \right \} \right \}\right \}$ $P(P(\phi ))$
answered
Jul 1
in
Set Theory & Algebra
by
srestha
Veteran
(
114k
points)

18
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
28
Kenneth Rosen Edition 7th Exercise 2.1 Question 24 (Page No. 126)
Determine whether each of these sets is the power set of a set, where $a$ and $b$ are distinct elements. $\phi$ $\left \{ \phi ,\left \{ a \right \} \right \}$ $\left \{ \phi ,\left \{ a \right \},\left \{ \phi ,a \right \} \right \}$ $\left \{ \phi ,\left \{ a \right \},\left \{ b \right \},\left \{ a,b \right \} \right \}$
answered
Jul 1
in
Set Theory & Algebra
by
srestha
Veteran
(
114k
points)

20
views
kennethrosen
discretemathematics
settheory&algebra
+18
votes
5
answers
29
GATE20022.17
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetric Symmetric and reflexive Transitive and reflexive Transitive and symmetric
answered
Jun 23
in
Set Theory & Algebra
by
pritishc
(
215
points)

2.7k
views
gate2002
settheory&algebra
normal
relations
+9
votes
3
answers
30
GATE19982.4
In a room containing $28$ people, there are $18$ people who speak English, $15$, people who speak Hindi and $22$ people who speak Kannada. $9$ persons speak both English and Hindi, $11$ persons speak both Hindi and Kannada whereas $13$ persons speak both Kannada and English. How many speak all three languages? $9$ $8$ $7$ $6$
answered
Jun 18
in
Set Theory & Algebra
by
Nithin2698
(
45
points)

1.2k
views
gate1998
settheory&algebra
easy
sets
+10
votes
4
answers
31
GATE19891iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
answered
Jun 18
in
Set Theory & Algebra
by
mohan123
Junior
(
759
points)

756
views
gate1989
settheory&algebra
relations
descriptive
+2
votes
1
answer
32
GATE19994
Let $G$ be a finite group and $H$ be a subgroup of $G$. For $a \in G$, define $aH=\left\{ah \mid h \in H\right\}$. Show that $aH = bH.$ Show that for every pair of elements $a, b \in G$, either $aH = bH$ or $aH$ and $bH$ are disjoint. Use the above to argue that the order of $H$ must divide the order of $G.$
answered
Jun 16
in
Set Theory & Algebra
by
Satbir
Boss
(
18k
points)

500
views
gate1999
settheory&algebra
groups
normal
cosets
+8
votes
3
answers
33
TIFR2011B23
Suppose $(S_{1}, S_{2},\ldots,S_{m})$ is a finite collection of nonempty subsets of a universe $U.$ Note that the sets in this collection need not be distinct. Consider the following basic step to be performed on this sequence. While there exist sets $S_{i}$ and ... of a finite universe $U$ and a choice of $S_{i}$ and $S_{j}$ in each step such that the process does not terminate.
answered
Jun 16
in
Set Theory & Algebra
by
Arjun
Veteran
(
418k
points)

382
views
tifr2011
settheory&algebra
sets
+16
votes
3
answers
34
GATE199811
Suppose $A = \{a, b, c, d\}$ and $\Pi_1$ is the following partition of A $\Pi_1 = \left\{\left\{a, b, c\right\}\left\{d\right\}\right\}$ List the ordered pairs of the equivalence relations induced by $\Pi_1$. Draw the graph of the above equivalence relation ... $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.
answered
Jun 15
in
Set Theory & Algebra
by
Satbir
Boss
(
18k
points)

1.8k
views
gate1998
settheory&algebra
normal
partialorder
descriptive
+7
votes
1
answer
35
TIFR2018B10
For two $n$ bit strings $x,y \in\{0,1\}^{n},$ define $z=x\oplus y$ to be the bitwise XOR of the two strings (that is, if $x_{i},y_{i},z_{i}$ denote the $i^{th}$ bits of $x,y,z$ respectively, then $z_{i}=x_{i}+y_{i} \bmod 2$ ... The number of such linear functions for $n \geq 2$ is: $2^{n}$ $2^{n^{2}}$ $\large2^{\frac{n}{2}}$ $2^{4n}$ $2^{n^{2}+n}$
answered
Jun 14
in
Set Theory & Algebra
by
Arjun
Veteran
(
418k
points)

236
views
tifr2018
functions
+1
vote
2
answers
36
GATE199017c
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.
answered
Jun 8
in
Set Theory & Algebra
by
Arjun
Veteran
(
418k
points)

248
views
gate1990
descriptive
settheory&algebra
lattice
+7
votes
1
answer
37
GATE19879e
How many true inclusion relations are there of the from $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
answered
Jun 7
in
Set Theory & Algebra
by
Arjun
Veteran
(
418k
points)

464
views
gate1987
settheory&algebra
relations
+1
vote
1
answer
38
GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
answered
Jun 6
in
Set Theory & Algebra
by
Arjun
Veteran
(
418k
points)

168
views
gate1995
settheory&algebra
numericalanswers
sets
0
votes
0
answers
39
Doubt on a math question
Chk this question https://gateoverflow.in/100202/testseriescounting $1)$Can someone verify this ans?? See if $\left ( _{0}^{6}\textrm{C} \right )$ in one set, other set will contain $\left ( _{6}^{6}\textrm{C} \right )$ elements. right?? Now why do we again need $2^{n}$ ... meaning of it?? $2)$ How $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{ni}=3^{n}$??
asked
Jun 4
in
Set Theory & Algebra
by
srestha
Veteran
(
114k
points)

29
views
discretemathematics
settheory&algebra
0
votes
0
answers
40
Ace booklet functions page:152 q.no 44
Let A, B, C are k element sets and let S be an n element set where k<=n. How many triples of functions f:A>S, g:B>S, h:C>S are there such that f, g and h are all injective and f(A) =g(B) =h(C) =?
asked
May 27
in
Set Theory & Algebra
by
chandan2teja
(
131
points)

23
views
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