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Recent questions tagged sets
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1
ISRO202076
If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$ Then $(A \cup B’) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ \ \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$
asked
Jan 13
in
Set Theory & Algebra
by
Satbir
Boss
(
24k
points)

134
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isro2020
discretemathematics
settheory&algebra
sets
easy
+1
vote
1
answer
2
ISI2014DCG5
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, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

95
views
isi2014dcg
sets
+2
votes
1
answer
3
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, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

49
views
isi2014dcg
sets
algebra
+1
vote
1
answer
4
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, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

37
views
isi2014dcg
sets
disjointsets
+1
vote
2
answers
5
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, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

49
views
isi2015mma
sets
subsets
+1
vote
2
answers
6
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, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

33
views
isi2015mma
sets
cartesianproduct
+1
vote
2
answers
7
ISI2015MMA8
Let $A$ be a set of $n$ elements. The number of ways, we can choose an ordered pair $(B,C)$, where $B,C$ are disjoint subsets of $A$, equals $n^2$ $n^3$ $2^n$ $3^n$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
431k
points)

46
views
isi2015mma
permutationandcombination
sets
0
votes
0
answers
8
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, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

11
views
isi2015mma
sets
functions
nongate
0
votes
0
answers
9
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, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

18
views
isi2015mma
sets
nongate
0
votes
2
answers
10
ISI2015DCG17
The set $\{(x,y): \mid x \mid + \mid y \mid \leq 1\}$ is represented by the shaded region in
asked
Sep 18, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

19
views
isi2015dcg
sets
0
votes
1
answer
11
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

13
views
isi2015dcg
sets
0
votes
0
answers
12
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

20
views
isi2015dcg
sets
functions
0
votes
1
answer
13
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

15
views
isi2016dcg
sets
functions
0
votes
0
answers
14
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

12
views
isi2016dcg
sets
0
votes
1
answer
15
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

16
views
isi2016dcg
sets
functions
0
votes
0
answers
16
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

12
views
isi2016dcg
sets
functions
0
votes
1
answer
17
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

17
views
isi2017dcg
sets
+1
vote
1
answer
18
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

30
views
isi2018dcg
sets
+1
vote
2
answers
19
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

49
views
isi2018dcg
sets
+5
votes
2
answers
20
GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
asked
Jun 6, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

412
views
gate1995
settheory&algebra
numericalanswers
sets
0
votes
0
answers
21
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, 2019
in
Set Theory & Algebra
by
aditi19
Active
(
5.2k
points)

74
views
kennethrosen
discretemathematics
relations
settheory&algebra
sets
+1
vote
0
answers
22
Which Statement is correct for the given sets statements
If A, B, C are three sets then which of the following is TRUE ? If ( A ∩ C ) = ( B ∩ C ) then A = B If ( A ∪ C ) = ( B ∪ C ) then A = B If ( A 𝜟 C ) = ( B 𝜟 C ) then A = B If ( A – C ) = ( B – C ) then A = B
asked
May 10, 2019
in
Set Theory & Algebra
by
pranay91331
(
73
points)

71
views
settheory&algebra
sets
discretemathematics
0
votes
1
answer
23
Self doubt group theory
Is (Z+,>=) a well oerderd set ,plz explain.
asked
Apr 17, 2019
in
Set Theory & Algebra
by
Manoj Kumar Pandey
(
281
points)

58
views
sets
0
votes
2
answers
24
Michael Sipser Edition 3 Exercise 0 Question 5 (Page No. 26)
If C is a set with c elements, how many elements are in the power set of C? Explain your answer.
asked
Apr 13, 2019
in
Theory of Computation
by
Lakshman Patel RJIT
Veteran
(
59k
points)

41
views
michaelsipser
theoryofcomputation
sets
easy
0
votes
1
answer
25
Michael Sipser Edition 3 Exercise 0 Question 4 (Page No. 26)
If A has a elements and B has b elements, how many elements are in A × B? Explain your answer.
asked
Apr 13, 2019
in
Theory of Computation
by
Lakshman Patel RJIT
Veteran
(
59k
points)

26
views
michaelsipser
theoryofcomputation
sets
easy
0
votes
0
answers
26
Michael Sipser Edition 3 Exercise 0 Question 3 (Page No. 26)
Let A be the set {x, y, z} and B be the set {x, y}. a. Is A a subset of B? b. Is B a subset of A? c. What is A ∪ B? d. What is A ∩ B? e. What is A × B? f. What is the power set of B?
asked
Apr 13, 2019
in
Theory of Computation
by
Lakshman Patel RJIT
Veteran
(
59k
points)

19
views
michaelsipser
theoryofcomputation
sets
easy
+1
vote
3
answers
27
Turing Machine Self Doubt
Can someone explain in details how set of all TM is countable?
asked
Mar 23, 2019
in
Theory of Computation
by
aditi19
Active
(
5.2k
points)

88
views
turingmachine
theoryofcomputation
counting
sets
+1
vote
1
answer
28
Gateforum Test Series: Set Theory & Algebra  Sets
asked
Jan 9, 2019
in
Set Theory & Algebra
by
Gupta731
Active
(
4.8k
points)

100
views
gateforumtestseries
settheory&algebra
sets
0
votes
0
answers
29
Zeal Test Series 2019: Set Theory & Algebra  Sets
asked
Dec 22, 2018
in
Set Theory & Algebra
by
Prince Sindhiya
Loyal
(
5.9k
points)

108
views
discretemathematics
settheory&algebra
sets
zeal
zeal2019
+3
votes
6
answers
30
TIFR2019A1
Let $X$ be a set with $n$ elements. How many subsets of $X$ have odd cardinality? $n$ $2^n$ $2^{n/2}$ $2^{n1}$ Can not be determined without knowing whether $n$ is odd or even
asked
Dec 18, 2018
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

617
views
tifr2019
engineeringmathematics
discretemathematics
settheory&algebra
sets
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