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Recent questions tagged settheory&algebra
Webpage for Set Theory & Algebra:
0
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1
Set theory
i am not able to understand the proof. How we reached statement 2 from statement 1 as I have marked in the picture (right side) Can some one elaborate?
asked
Mar 14
in
Mathematical Logic
by
Sandy Sharma
Active
(
1.3k
points)

36
views
settheory&algebra
discretemathematics
0
votes
1
answer
2
General Topic Doubt Set Theory & Algebra: Relations
How to check a relation is transitive or not from its matrix representation? Please help me with an example.
asked
Mar 8
in
Set Theory & Algebra
by
Sona Barman
Active
(
1.3k
points)

73
views
settheory&algebra
discretemathematics
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generaltopicdoubt
+1
vote
1
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3
Ace Test Series: Set Theory & Algebra  Relations
Let $A=\left \{ 1,2,3 \right \}$. Number of relation on $A$ which are neither reflexive, nor irreflexive but symmetric is ___________ Ans given 48 but I got 8 Please verify
asked
Mar 7
in
Set Theory & Algebra
by
srestha
Veteran
(
109k
points)

118
views
acetestseries
engineeringmathematics
discretemathematics
settheory&algebra
relations
0
votes
1
answer
4
Kenneth Rosen Edition 6th Exercise 2.3 Question 36 (Page No. 147)
Let f be a function from the set A to the set B.Let S and T be subsets of A.Show that $f(S\cup T)=f(S)\cup f(T)$ $f(S\cap T)\subseteq f(S)\cap f(T)$ Show that inclusion in part b can be proper
asked
Feb 18
in
Set Theory & Algebra
by
himgta
Active
(
3.8k
points)

63
views
kennethrosen
settheory&algebra
discretemathematics
0
votes
1
answer
5
JEST Sample Question 1a
Let a and b be positive integers such that a > b and a^ 2 − b^ 2 is a prime number. Then a^2 − b^ 2 is equal to (A) a − b (B) a + b (C) a × b (D) none of the above
asked
Feb 15
in
Set Theory & Algebra
by
sripo
Active
(
1.5k
points)

65
views
jest
discretemathematics
settheory&algebra
+2
votes
1
answer
6
JEST Sample Question 1b
When is the following statement true? (A ∪ B) ∩ C = A ∩ C (A) If Ā ∩ B ∩ C = φ (B) If A ∩ B ∩ C = φ (C) always (D) never
asked
Feb 15
in
Set Theory & Algebra
by
sripo
Active
(
1.5k
points)

66
views
jest
discretemathematics
settheory&algebra
0
votes
1
answer
7
Jest Exam sample question3
How many subsets of even cardinality does an nelement set have ? Justify answer. Please give a proof if possible.This is part of subjective JEST paper.
asked
Feb 15
in
Set Theory & Algebra
by
sripo
Active
(
1.5k
points)

23
views
jest
settheory&algebra
discretemathematics
+2
votes
4
answers
8
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
in
Set Theory & Algebra
by
Arjun
Veteran
(
386k
points)

2k
views
gate2019
engineeringmathematics
discretemathematics
settheory&algebra
groups
+1
vote
1
answer
9
MadeEasy Test Series 2019: Discrete Mathematics  Set Theory & Algebra
Which of the following are Well ordered set $\left [ Z^{+},\leq \right ]$ $\left [ Z^{},\leq \right ]$ $\left [ Z^{+},\geq \right ]$ $\left [ Z^{},\geq \right ]$
asked
Jan 28
in
Set Theory & Algebra
by
jatin khachane 1
Loyal
(
6.4k
points)

138
views
madeeasytestseries
settheory&algebra
0
votes
0
answers
10
Testbook.com
Let f be a function from A to B and f 1 exist. Let S and T be subsets of B. Which of the following is true? 1. f 1 (S ∪ T) = f 1 (S) ∪ f 1 (T) 2. f 1 (S ∩ T) = f 1 (S) ∩ f 1 (T)
asked
Jan 27
in
Mathematical Logic
by
Rishav Chetan
(
41
points)

20
views
settheory&algebra
0
votes
1
answer
11
MadeEasy Test Series: Set Thoery & Algebra  Partial Order
Let Q denote the set of rational numbers and S = {x  x belongs N ; N; x>=10} Consider the Following POSETs I. (Q ∩ [0, 1], ≤) II. (S, ≤) Which of the above POSETs are well ordered?
asked
Jan 26
in
Set Theory & Algebra
by
Badayayash
Junior
(
889
points)

112
views
settheory&algebra
partialorder
madeeasytestseries
0
votes
0
answers
12
Made Easy Test Series 2019: Set theory & Algebra  Groups
set of all possible diagonal matrix of order n ans given monoid my doubtwhy it cannot have inverse??
asked
Jan 24
in
Set Theory & Algebra
by
priyanka manwani
(
375
points)

51
views
discretemathematics
settheory&algebra
groups
madeeasytestseries2019
madeeasytestseries
0
votes
1
answer
13
Functions and Relations
What is the number of relations S over set {0,1,2,3} such that (x,y) $\epsilon$ S $\Rightarrow x = y$ ? Thanks.
asked
Jan 23
in
Set Theory & Algebra
by
Abhipsa Mishra
(
149
points)

47
views
settheory&algebra
relations
functions
discretemathematics
0
votes
1
answer
14
Functions
What Is The Total Number Of Boolean Functions Possible Over N Boolean Variables?
asked
Jan 23
in
Set Theory & Algebra
by
Abhipsa Mishra
(
149
points)

37
views
discretemathematics
functions
settheory&algebra
0
votes
1
answer
15
Relations
Consider the following relation: $R={(x,y) y=x^i, ∃ “i” in Z }$ R is i) Reflexive ii) Symmetric iii) Anti symmetric iv) Transitive Thanks!
asked
Jan 23
in
Set Theory & Algebra
by
Abhipsa Mishra
(
149
points)

34
views
settheory&algebra
relations
discretemathematics
0
votes
1
answer
16
GATEBOOK2019 Mock Test111
Let $S, T,$ and $U$ be nonempty sets, and let $f : S\to T$ and $g : T \to U$ be functions such that the function $g o f : S \to U$ is onetoone (injective). Which of the following must be TRUE? $f$ is onetoone. $f$ is onto. $g$ is onetoone. $g$ is onto.
asked
Jan 19
in
Others
by
GATEBOOK
Boss
(
15.3k
points)

212
views
gb2019mock1
discretemathematics
settheory&algebra
0
votes
0
answers
17
group
if (G,*) is a cyclic group of order 97 , then number of generator of G is equal to ___
asked
Jan 16
in
Set Theory & Algebra
by
Rahul_Rathod_
Junior
(
565
points)

79
views
groups
discretemathematics
settheory&algebra
0
votes
0
answers
18
Groups
How G = ( 1,1,i,  i ) under multiplication is Group? H = ( i, i ) is subgroup under multiplication? Please suggest
asked
Jan 15
in
Set Theory & Algebra
by
Mayankprakash
Active
(
1.1k
points)

37
views
settheory&algebra
subgroups
groups
discretemathematics
0
votes
0
answers
19
Madeeasy CBT1
asked
Jan 13
in
Set Theory & Algebra
by
jatin khachane 1
Loyal
(
6.4k
points)

159
views
settheory&algebra
0
votes
0
answers
20
Composition of a relation Madeeasy 2019
How to take composition of a Relation? here used concept of function but when to go with the transitivity rule concept as mentioned below? Please clarify in general when to use which method
asked
Jan 10
in
Mathematical Logic
by
Markzuck
Junior
(
633
points)

43
views
discretemathematics
relations
functions
settheory&algebra
0
votes
0
answers
21
MadeEasy Test Series: Set Theory & Algebra  Relations
asked
Jan 10
in
Mathematical Logic
by
Shankar Kakde
(
369
points)

46
views
madeeasytestseries
settheory&algebra
relations
+1
vote
1
answer
22
Gateforum Test Series: Set Theory & Algebra  Sets
asked
Jan 9
in
Set Theory & Algebra
by
Gupta731
Active
(
4.5k
points)

60
views
gateforumtestseries
settheory&algebra
sets
0
votes
0
answers
23
Abelian Group
Prove with examples: The set of all rational numbers except 0 are abelian group under multiplication. The set of all real numbers except 0 are closed under abelian group under multiplication.
asked
Jan 8
in
Set Theory & Algebra
by
Shamim Ahmed
Active
(
2.3k
points)

25
views
abeliangroup
settheory&algebra
0
votes
1
answer
24
Reflexive Relation
Can anyone help …. where I am wrong…??
asked
Jan 8
in
Mathematical Logic
by
Vikas123
(
359
points)

44
views
relations
settheory&algebra
discretemathematics
+1
vote
0
answers
25
#set theory #groups
Consider the set H of all 3 × 3 matrices of the type: $\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$ where a, b, c, d, e and f are real numbers and $abc ≠ 0$. Under the matrix multiplication operation, the set H is: (a) a group (b) a monoid but not a group (c) a semigroup but not a monoid (d) neither a group nor a semigroup
asked
Jan 5
in
Set Theory & Algebra
by
Kunal Kadian
Active
(
2.6k
points)

56
views
settheory&algebra
groups
matrices
0
votes
0
answers
26
Determine whether the relation is reflexive, symmetric, and/or transitive?
Let R be the relation on the set ‘N’ of strictly positive integers, where strictly positive integers x and y satisfy x R y iff x^2 – y^2 = 2^k for some nonnegative integer k. Which of the following statement is true with respect to R? I think it’s just reflexive, because it obeys reflexive conditions.
asked
Jan 2
in
Mathematical Logic
by
susgir2
Active
(
1.4k
points)

44
views
settheory&algebra
relations
discretemathematics
0
votes
2
answers
27
Zeal Test Series 2019: Set Theory & Algebra  Relations
The Number of Relations, Which are both Reflexive and Symmetric but not AntiSymmetric, on a set with 6 elements, are ____________? i got 32768 plz check
asked
Jan 2
in
Set Theory & Algebra
by
Prince Sindhiya
Loyal
(
6.2k
points)

53
views
zeal
discretemathematics
settheory&algebra
relations
zeal2019
0
votes
1
answer
28
Ace academy test series
Ans:C. Please explain
asked
Dec 28, 2018
in
Combinatory
by
amitqy
Active
(
1.7k
points)

92
views
settheory&algebra
permutationsandcombinations
testseries
0
votes
2
answers
29
Ace Test Series: Set Theory & Algebra  Relations
Ans:B Symmetric closure of R 1. It is symmetric 2. It contains R 3.Minimal relation satisfying 1 and 2 If we consider B, then condition 2 may be violated. Therefore I think the answer should be D.
asked
Dec 26, 2018
in
Set Theory & Algebra
by
amitqy
Active
(
1.7k
points)

96
views
acetestseries
settheory&algebra
relations
+1
vote
0
answers
30
Number of AntiSymmetric Relations
Number of possible AntiSymmetric relations possible on a set of Size 5 whose size is maximum? My Work: Whose Size is maximum means, we should take all reflexive pairs. Okay, now we are left with $\frac{n(n1)}{2}$ offdiagonal pairs. We can have 3 ... must be $3^{\binom{5}{2}}$ But the answer was given to be 1024. Please guide me to the correct thought process.
asked
Dec 25, 2018
in
Mathematical Logic
by
Ayush Upadhyaya
Boss
(
24.9k
points)

83
views
relations
settheory&algebra
discretemathematics
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