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Recent questions tagged settheory
+1
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1
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1
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
in
Set Theory & Algebra
by
Arjun
Veteran
(
424k
points)

31
views
isi2014dcg
settheory
algebra
0
votes
1
answer
2
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
in
Set Theory & Algebra
by
Arjun
Veteran
(
424k
points)

18
views
isi2014dcg
settheory
disjointsets
+1
vote
2
answers
3
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
in
Set Theory & Algebra
by
Arjun
Veteran
(
424k
points)

40
views
isi2015mma
settheory
subsets
+1
vote
2
answers
4
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
in
Set Theory & Algebra
by
Arjun
Veteran
(
424k
points)

24
views
isi2015mma
settheory
cartesianproduct
0
votes
0
answers
5
ISI2015MMA23
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X$. Define $f: X \times \mathcal{P}(X) \to \mathbb{R}$ by $f(x,A)=\begin{cases} 1 & \text{ if } x \in A \\ 0 & \text{ if } x \notin A \end{cases}$ Then $f(x, A \cup B)$ ... $f(x,A)+f(x,B)\:  f(x,A) \cdot f(x,B)$ $f(x,A)\:+ \mid f(x,A)\:  f(x,B) \mid $
asked
Sep 23
in
Set Theory & Algebra
by
Arjun
Veteran
(
424k
points)

5
views
isi2015mma
settheory
functions
nongate
0
votes
0
answers
6
ISI2015MMA31
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1 \} \:\:\:\:\:\:\:\: B = \{ (x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is nonempty none of the above
asked
Sep 23
in
Set Theory & Algebra
by
Arjun
Veteran
(
424k
points)

9
views
isi2015mma
settheory
nongate
0
votes
1
answer
7
ISI2015DCG35
Let $A$, $B$ and $C$ be three non empty sets. Consider the two relations given below: $\begin{array}{lll} A(BC)=(AB) \cup C & & (1) \\ A – (B \cup C) = (A B)C & & (2) \end{array}$ Both $(1)$ and $(2)$ are correct $(1)$ is correct but $(2)$ is not $(2)$ is correct but $(1)$ is not Both $(1)$ and $(2)$ are incorrect
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

8
views
isi2015dcg
settheory
sets
+1
vote
1
answer
8
ISI2015DCG36
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$. The number of bijective functions from $X$ to $Y$ is $n^n$ $n \log_2 n$ $n^2$ $n!$
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

15
views
isi2015dcg
settheory
functions
0
votes
0
answers
9
ISI2015DCG37
Suppose $f_{\alpha} : [0,1] \to [0,1],\:\: 1 < \alpha < \infty$ is given by $f_{\alpha} (x) = \frac{(\alpha +1)x}{\alpha x+1}$ Then $f_{\alpha}$ is A bijective (oneone and onto) function A surjective (onto ) function An injective (oneone) function We cannot conclude about the type
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

14
views
isi2015dcg
settheory
functions
0
votes
1
answer
10
ISI2016DCG27
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of triangle $x,$ is oneone and into oneone and onto manyone and onto manyone and into
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

7
views
isi2016dcg
settheory
functions
0
votes
0
answers
11
ISI2016DCG35
Let $A,B$ and $C$ be three non empty sets. Consider the two relations given below: $A(BC)=(AB)\cup C$ $A(B\cup C)=(AB)C$ Both (1) and (2) are correct. (1) is correct but (2) is not. (2) is correct but (1) is not. Both (1) and (2) are incorrect.
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

7
views
isi2016dcg
settheory
sets
0
votes
1
answer
12
ISI2016DCG36
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$.. The number of bijective functions from $X$ to $Y$ is $n^{n}$ $n\log_{2}n$ $n^{2}$ $n!$
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

8
views
isi2016dcg
settheory
functions
0
votes
0
answers
13
ISI2016DCG37
Suppose $f_{\alpha}\::\:[0,1]\rightarrow[0,1],\:1<\alpha<\infty$ is given by $f_{\alpha}(x)=\dfrac{(\alpha+1)x}{\alpha x+1}.$ Then $f_{\alpha}$ is A bijective (oneone and onto) function. A surjective (onto) function. An injective (oneone) function. We can not conclude about the type.
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

3
views
isi2016dcg
settheory
functions
0
votes
1
answer
14
ISI2017DCG12
Two sets have $m$ and $n$ elements. The number of subsets of the first set is $96$ more than that of the second set. Then the values of $m$ and $n$ are $8$ and $6$ $7$ and $6$ $7$ and $5$ $6$ and $5$
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

6
views
isi2017dcg
settheory
sets
+1
vote
1
answer
15
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
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

19
views
isi2018dcg
settheory
sets
primenumbers
+1
vote
2
answers
16
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
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

34
views
isi2018dcg
settheory
sets
0
votes
0
answers
17
Rosen 7e Exercise9.6 Question no27 page no631
What is the covering relation of the partial ordering {(A, B)  A ⊆ B} on the power set of S, where S = {a, b, c}? i'm getting R={(Ф, {a}), (Ф, {b}), (Ф, {c}), (Ф, {a, b}), (Ф, {b, c}), (Ф, {a, c}), (Ф, {a, b, c}), ({a}, {a, b}), ({a}, {a, c}), ({b}, ... b, c}), ({c}, {a, c}), ({c}, {b, c}), ({a, b}, {a, b, c}), ({a, c}, {a, b, c})({b, c}, {a, b, c})
asked
May 10
in
Set Theory & Algebra
by
aditi19
Active
(
5.1k
points)

67
views
kennethrosen
discretemathematics
relations
settheory&algebra
settheory
sets
+1
vote
3
answers
18
Turing Machine Self Doubt
Can someone explain in details how set of all TM is countable?
asked
Mar 23
in
Theory of Computation
by
aditi19
Active
(
5.1k
points)

77
views
turingmachine
theoryofcomputation
counting
settheory
+1
vote
1
answer
19
#relation
The Number of Relations, Which are both Reflexive and Symmetric but not AntiSymmetric, on a set with 6 elements, are ____________?
asked
Dec 3, 2018
in
Set Theory & Algebra
by
Satbir
Boss
(
21.6k
points)

134
views
settheory
0
votes
1
answer
20
Set Theory
If A = {1,2,3...n}, then number of equivalence relations possible on A , which are also surjection on A is ________________? How to approach this type of problems?
asked
Nov 9, 2018
in
Set Theory & Algebra
by
dan31
Junior
(
883
points)

104
views
discretemathematics
settheory&algebra
settheory
0
votes
1
answer
21
Set Theory
A relation R on a set of positive integers is defined by (a,b) belongs to R iff a and b are relatively prime. Which of the following is true about R? a. Symmetric and Reflexive b. Symmetric and irreflexive c.Symmetric and transitive d. Symmetric and not transitive The Ans is given as (d) but I think (b) is true. Any thoughts?
asked
Nov 8, 2018
in
Set Theory & Algebra
by
dan31
Junior
(
883
points)

85
views
discretemathematics
settheory&algebra
settheory
engineeringmathematics
sets
+1
vote
1
answer
22
ISI2017PCBA3
Let $B=\{1, 2, 3, 4\}$. A set $S \subseteq B \times B$ called a symmetric set of $B$ if for all $x, y \in B$, $ (x, y) \in S \Rightarrow (y,x) \in S.$ Find the number of symmetric sets of $B$.
asked
Sep 19, 2018
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

26
views
isi2017pcba
settheory
relations
symmetric
descriptive
0
votes
1
answer
23
ISI2016MMA13
Which one of the following statements is correct regarding the elements and subsets of the set $\{1, 2, \{1, 2, 3\}\}$? $\{1, 2\} \in \{1, 2, \{1, 2, 3\} \}$ $\{1, 2\} \subseteq \{1, 2, \{1, 2, 3\} \}$ $\{1, 2, 3\} \subseteq \{1, 2, \{1, 2, 3\} \}$ $3 \in \{1, 2, \{1, 2, 3\} \}$
asked
Sep 13, 2018
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

12
views
isi2016mmamma
settheory
sets
subsets
0
votes
0
answers
24
Set Theory Doubt
What is meant by s* or any other symbol which has an asterisk in Set Theory?
asked
Aug 12, 2018
in
Set Theory & Algebra
by
Devshree Dubey
Boss
(
13.7k
points)

54
views
discretemathematics
settheory
0
votes
1
answer
25
Set Theory
How to distinguish between countably finite , countably infinite , uncountably infinite set? for reference see this ques:https://gateoverflow.in/36654/whysetofallfunctionsfn01isuncountablyinfinite
asked
May 15, 2018
in
Set Theory & Algebra
by
srestha
Veteran
(
117k
points)

298
views
discretemathematics
settheory&algebra
settheory
sets
engineeringmathematics
0
votes
1
answer
26
Set theory
Consider the sets $A_1, A_2, A_3 \dots A_m$. Prove that the number of distinct sets of the form $A_i \oplus A_j$ is at least $m$.
asked
Apr 28, 2018
in
Set Theory & Algebra
by
dd
Veteran
(
57k
points)

64
views
settheory
combinatoricsiitb
0
votes
0
answers
27
Set theory and Induction
Consider the set of all subsets of a set S. A chain is a collection of subsets $P_1 \subset P_2 \subset P_3 \subset P_4 \dots \subset P_k$. A symmetric chain is one which starts at a set of size $i$ and ends at a set of size $n  i$. Prove that the poset has a decomposition into symmetric chains.
asked
Apr 28, 2018
in
Set Theory & Algebra
by
dd
Veteran
(
57k
points)

46
views
settheory
combinatoricsiitb
0
votes
0
answers
28
Probability and set theory
Consider sets $A_1,A_2,A_3 \text{ to } A_m \text{ where }A_i \subseteq [n] \text{ and } [n] = \{1,2,3, \dots n \}$ such that there are no three distinct sets in the collection with the property $A_i \subset A_j \subset A_k.$ For even $n$, prove that \begin{align*} m ... bound on $m$ : \begin{align*} m \leq \binom{n}{\frac{n}{2}} + \binom{n}{\frac{n}{2}  1} \end{align*}
asked
Apr 27, 2018
in
Set Theory & Algebra
by
dd
Veteran
(
57k
points)

38
views
probability
settheory
combinatoricsiitb
+3
votes
1
answer
29
Previous year
A survey on a sample of $25$ new cars being sold at a local auto dealer was conducted to see which of the three popular optionsair conditioning, radio and power windows were already installed. The survey found : $15$ had air conditioning, $2$ had air conditioning and power ... $3$ had all three options. What is the number of cars that had none of the options? $4$ $3$ $1$ $2$
asked
Mar 9, 2018
in
Numerical Ability
by
Raj Kumar 7
Active
(
1.1k
points)

159
views
generalaptitude
numericalability
settheory
+2
votes
1
answer
30
Set theory
Let $f: A \to B$ be a function and $S$ and $T$ be subsets of $B$. Consider the following statements about image (range) : $S1:\quad f^{1}(S \cup T) = f^{1}(S) \cup f^{1}(T)$ $S2:\quad f^{1}(S \cap T) = f^{1}(S) \cap f^{1}(T)$ Which of the following is correct? A) only S1 is true B) only S2 is true C) Both S1 and S2 is true D) Neither S1 nor S2 is true
asked
Dec 31, 2017
in
Set Theory & Algebra
by
ashish pal
Junior
(
823
points)

143
views
discretemathematics
settheory&algebra
sets
engineeringmathematics
settheory
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