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Recent questions and answers in Set Theory & Algebra
0
votes
1
answer
ACE handbook
Suppose that S is a set with n elements. How many ordered pairs (A , B) are there such that A and B are subsets of S and A is subset of B? 1. 2^n 2. 3^n 3.n^2 4.C(n , 2)
answered
Oct 17
in
Set Theory & Algebra
by
mayureshpatle
(
855
points)

44
views
0
votes
0
answers
Gatebook function
How to solve this type of question ?
asked
Oct 2
in
Set Theory & Algebra
by
Raj_81
(
5
points)

15
views
discretemaths
functions
0
votes
0
answers
UGC NET 2016 as well as Discrete Maths Kenneth Rosen PAGE Pg 657 Q21
[closed]
asked
Sep 15
in
Set Theory & Algebra
by
Shashank Rustagi
(
513
points)

22
views
kennethrosen
combinatory
0
votes
1
answer
#Self_Doubt #Settheory #GATECSE2015
Suppose L={p,q,r,s,t}L={p,q,r,s,t} is a lattice represented by the following Hasse diagram: For any x,y∈Lx,y∈L, not necessarily distinct , x∨y and x∧y are join and meet of x,y respectively. Let L3={(x,y,z):x,y,z∈L} be the set of all ordered ... )∧(x∨z) for L1* and L2* respectively. Then (A) P1>P2 (B) P1<P2 (C) P1=P2 (D) none which one should be correct?
answered
Aug 27
in
Set Theory & Algebra
by
suvradip das
(
113
points)

28
views
0
votes
0
answers
DU MCA Entrance 2017
If A is a 3*3 Matrix with Eigenvalues 2 and 1 and the respective Eigenvectors (1 2 0) and (0 0 1), then the vectors A^3 (1 2 2) is equal to ; ( 8 16 6) (2 4 2) (8 16 1) (8 16 2)
asked
Aug 25
in
Set Theory & Algebra
by
Jatin99
(
5
points)

16
views
+1
vote
1
answer
LATTICE ASSOCIATIVITY DOUBT
I wasn't convinced about the associativity property of lattices, and the proof i found on math.stackexchange seemed reasonable, but still i couldnt wrap my head around it. I tried to make a counter example, and in the above diagram (b join c) ... otherwise it would've satisfied associativity. But i cant seem to figure out why this diagram isn't a lattice. Please help.
answered
Aug 25
in
Set Theory & Algebra
by
varsha394
(
11
points)

47
views
discretemaths
settheory&algebra
selfdoubt
0
votes
1
answer
ISI CSB 2018
State, with justification, which of the following expressions f, g and h, define valid realvalued functions over the set of positive rational numbers. We denote a rational number by m/n, where m and n are positive integers. (a) f(m/n) = 2^m − 2^n. (b) g(m/n) = log m − log n. (c) h(m/n) = (m^2 − n^2)/(mn).
answered
Aug 20
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

25
views
discretemaths
sets
0
votes
1
answer
Kenneth rosen (7th edition) chapter 9
Let (S,R) be a poset.show that(S,$R^{1}$) is also a poset.where $R^{1}$ is the inverse of R.explain with example.
answered
Aug 16
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

16
views
0
votes
1
answer
Self problems
Lim x>0 [ (cosx  cos(sinx))/x^4 ]= ?? Please!! tell me the best approach to solve this question
answered
Aug 16
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

39
views
0
votes
1
answer
Kenneth Rosen 9.5 Exercise 15
Let R be the relation on the set of ordered pairs of positive integers such that ((a,b),(c,d)) ∈ R if and only if a+d = b+c. Show that R is an equivalence relation.
answered
Aug 16
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

34
views
kennethrosen
discretemaths
equivalencerelation
0
votes
2
answers
Group Theory Book
Any standard book for group theory numericals?
answered
Aug 16
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

72
views
grouptheory
theory
sets
0
votes
1
answer
#self doubt Function
Whether gof is one one for the picture given below?
answered
Aug 16
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

16
views
function
0
votes
1
answer
Discrete Maths
What if I have a function "X" and it's inverse "Y" can I guaranteed say that the function X is bijective? Or in simple terms can I say inverse of a function exists if and only if it's bijective?
answered
Aug 15
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

30
views
discretemaths
discretemaths
engineeringmaths
0
votes
1
answer
#disctete math function
Q.Let f(x) be a polynomial and g(x)=f'(x) be its derivatives . if the degree of (f(x)+f(x)) is 10, then degree of (g(x)+g(x)) is_________.
answered
Aug 15
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

11
views
function
questions
0
votes
1
answer
Show that given relation is an equivalence relation?
answered
Aug 15
in
Set Theory & Algebra
by
jayeshasawa001
(
2.5k
points)

48
views
equivalencerelation
sets
relation
0
votes
2
answers
Self doubt on relations and functions
Is x^3 injective or not in interval of all integers i.e. form  infinity to +infinity?Please explain.
answered
Aug 15
in
Set Theory & Algebra
by
jayeshasawa001
(
2.5k
points)

24
views
0
votes
1
answer
Is rings and fields in gate syllabus?
answered
Aug 15
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

56
views
0
votes
1
answer
madeeasy set theory
What is the meaning of symmetric relations are closed under complementation ..?Please cite an example..
answered
Aug 12
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

27
views
madeeasytestseries
0
votes
1
answer
Self doubt: Ordered Pair
What is meaning of ordered pair of rational numbers, or ordered pair of integers , or real numbers??
answered
Aug 12
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

54
views
discretemaths
0
votes
1
answer
Mathematics ME Test series
Ques: What is the number of partition of X = {a, b, c, d, e, f} where a and c are always in same block?  15  52  203  None of these
answered
Aug 12
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

27
views
discretemaths
madeeasytestseries
0
votes
1
answer
Relation :DiscreteMathGB
Let R be a relation from a set A to a set B. The inverse relation from B to A, denoted by , is the set of ordered pairs . S1: R is reflexive relation iff S2: R is a symmetric relation iff Which one of the following statements is true? (A).Only S1 (B).Only S2 (C).Both S1 and S2 (D).None
answered
Aug 11
in
Set Theory & Algebra
by
Arkaprava
(
711
points)

62
views
discretemaths
0
votes
1
answer
ISI CSB 2018
Given A = {1, 2, 3, .... , 70}, show that for any six elements a1, a2, a3, a4, a5 and a6 belonging to A, there exists one pair ai and aj for which ai − aj ≤ 14 (i not equals to j).
answered
Aug 11
in
Set Theory & Algebra
by
toxicdesire
(
459
points)

21
views
discretemaths
0
votes
0
answers
Discrete MathematicsFunctions
Let $A=\{1,2,3,4,5\},B=\{w,x,y,z\},A_{1}=\{2,3,5\}\subseteq A$ and $g:A_{1}\rightarrow B.$ In how many ways can $g$ be extended to a function $f:A\rightarrow B$
asked
Jul 25
in
Set Theory & Algebra
by
KUSHAGRA गुप्ता
(
1.4k
points)

42
views
discretemathematics
functions
0
votes
1
answer
Self Doubt : Lattice
$\left \{ 1,2,3,24,30 \right \}$ is it a lattice? I think this poset has no lub as $24$ and $30$ are not comparable. Am I right?
answered
Jul 22
in
Set Theory & Algebra
by
KUSHAGRA गुप्ता
(
1.4k
points)

58
views
lattice
discretemaths
0
votes
0
answers
ISI2015MCQ7
Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define the set R by R = {(x, y) ∈ X ×X : x and y have the same remainder when divided by 3}. Then the number of elements in R is (A) 40 (B) 36 (C) 34 (D) 33
asked
Jul 2
in
Set Theory & Algebra
by
suparna kar
(
9
points)

25
views
discretemathematics
sets
0
votes
1
answer
#DiscreteMaths Relationship between Equivalence classes of an equivalence relationship and partition of a set?
answered
May 26
in
Set Theory & Algebra
by
KUSHAGRA गुप्ता
(
1.4k
points)

27
views
sets
equivalencerelation
0
votes
0
answers
#EM Relations  Is this relation Transitive. May someone explain?
[closed]
asked
Apr 26
in
Set Theory & Algebra
by
iarnav
(
231
points)

18
views
relation
help
0
votes
0
answers
least upper bound and greatest lower bound
what are the greatest lower bound (glb) and the least upper bound (lub) of the sets a = {3, 9, 12} and b = {1, 2, 4, 5, 10} if they exist in Poset (z*,/)?
asked
Apr 19
in
Set Theory & Algebra
by
Shivshankar
(
5
points)

26
views
discretemaths
settheory
ugcnet2019
hassediagram
0
votes
0
answers
Kenneth Rosen 7th edition Chapter 9relations exercise 9.6
asked
Apr 19
in
Set Theory & Algebra
by
sriranjanivenkat99
(
5
points)

14
views
kennethrosen
relation
0
votes
0
answers
GATE2015139 Video Solution
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 $\left\{ \textit{g}\right\}$ ... $\left\{ \textit{g}\right\}$ is functionally complete Neither $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete
asked
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

7
views
gate20151
settheory&algebra
functions
difficult
videosolution
0
votes
0
answers
GATE19976.3 Video Solution
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
asked
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

6
views
gate1997
settheory&algebra
relations
normal
videosolution
0
votes
0
answers
GATE2015240 Video Solution
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
asked
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

2
views
gate20152
settheory&algebra
functions
normal
numericalanswers
videosolution
0
votes
0
answers
GATE2016128 Video Solution
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
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

8
views
gate20161
settheory&algebra
functions
normal
numericalanswers
videosolution
0
votes
0
answers
GATE20057 Video Solution
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
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

3
views
gate2005
settheory&algebra
normal
relations
videosolution
0
votes
0
answers
GATE200721 Video Solution
How many different nonisomorphic Abelian groups of order $4$ are there? $2$ $3$ $4$ $5$
asked
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

5
views
gate2007
grouptheory
normal
videosolution
0
votes
0
answers
GATE201827 Video Solution
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
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

10
views
gate2018
settheory&algebra
countableuncountableset
normal
videosolution
0
votes
0
answers
GATE2015134 Video Solution
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
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

6
views
gate20151
settheory&algebra
normal
lattice
videosolution
0
votes
0
answers
GATE2015116 Video Solution
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
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

5
views
gate20151
settheory&algebra
sets
normal
videosolution
0
votes
0
answers
GATE2016228 Video Solution
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 ... \ 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
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

9
views
gate20162
settheory&algebra
difficult
sets
videosolution
0
votes
0
answers
GATE2014350 Video Solution
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
Apr 18
in
Set Theory & Algebra
by
admin
(
193
points)

5
views
gate20143
settheory&algebra
grouptheory
numericalanswers
normal
videosolution
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