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JEST 2020
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that F is oneone For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.
asked
Feb 17
in
Set Theory & Algebra
by
vivek_mishra
Junior
(
585
points)

78
views
jest
functions
sets
+1
vote
1
answer
2
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 $(A \cup \bar{B}) \cap (A \cap B)$ 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
(
25.1k
points)

176
views
isro2020
discretemathematics
settheory&algebra
sets
easy
0
votes
1
answer
3
$\textbf{NTA NET DEC 2019 (group)}$
Consider the following statements: $\mathbf{S_1:}\;\;$If a group $\mathbf{(G,*)}$ is of order $\mathbf n$ and $\mathrm {a \in G}$ is such that $\mathrm {a^m=e}$ for some integer $\mathrm {m \le n}$ then $\mathbf m$ must divide $\mathbf n$ ... $(3)\;\;\;\text{Niether}\; \mathrm{S_1}\;\text{nor}\;\mathrm{S_2}$
asked
Dec 29, 2019
in
Set Theory & Algebra
by
Sanjay Sharma
Boss
(
49.4k
points)

126
views
ugcnetdec2019ii
grouptheory
+1
vote
1
answer
4
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
(
434k
points)

112
views
isi2014dcg
sets
+2
votes
1
answer
5
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
(
434k
points)

56
views
isi2014dcg
sets
algebra
+1
vote
1
answer
6
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
(
434k
points)

48
views
isi2014dcg
sets
disjointsets
+1
vote
2
answers
7
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
(
434k
points)

62
views
isi2015mma
sets
subsets
+1
vote
2
answers
8
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
(
434k
points)

41
views
isi2015mma
sets
cartesianproduct
0
votes
0
answers
9
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
(
434k
points)

20
views
isi2015mma
sets
functions
nongate
0
votes
0
answers
10
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
(
434k
points)

31
views
isi2015mma
sets
nongate
0
votes
0
answers
11
ISI2015MMA92
Consider the group $G=\begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{1} \end{pmatrix} : a,b \in \mathbb{R}, \: a>0 \end{Bmatrix}$ ... is of finite order $N$ is a normal subgroup and the quotient group is isomorphic to $\mathbb{R}^+$ (the group of positive reals with multiplication).
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
434k
points)

27
views
isi2015mma
grouptheory
subgroups
normal
nongate
0
votes
1
answer
12
ISI2015MMA93
Let $G$ be a group with identity element $e$. If $x$ and $y$ are elements in $G$ satisfying $x^5y^3=x^8y^5=e$, then which of the following conditions is true? $x=e, \: y=e$ $x\neq e, \: y=e$ $x=e, \: y \neq e$ $x\neq e, \: y \neq e$
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
434k
points)

30
views
isi2015mma
grouptheory
0
votes
1
answer
13
ISI2015MMA94
Let $G$ be the group $\{\pm1, \pm i \}$ with multiplication of complex numbers as composition. Let $H$ be the quotient group $\mathbb{Z}/4 \mathbb{Z}$. Then the number of nontrivial group homomorphisms from $H$ to $G$ is $4$ $1$ $2$ $3$
asked
Sep 23, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
434k
points)

24
views
isi2015mma
grouptheory
nongate
0
votes
2
answers
14
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
(
17.6k
points)

27
views
isi2015dcg
sets
+1
vote
1
answer
15
ISI2015DCG27
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
(
17.6k
points)

31
views
isi2015dcg
functions
0
votes
1
answer
16
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
(
17.6k
points)

18
views
isi2015dcg
sets
+2
votes
1
answer
17
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.6k
points)

26
views
isi2015dcg
functions
0
votes
0
answers
18
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
(
17.6k
points)

23
views
isi2015dcg
sets
functions
+1
vote
1
answer
19
ISI2015DCG49
The domain of the function $\text{ln}(3x^24x+5)$ is set of positive real numbers set of real numbers set of negative real numbers set of real numbers larger than $5$
asked
Sep 18, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.6k
points)

40
views
isi2015dcg
functions
0
votes
1
answer
20
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
(
17.6k
points)

24
views
isi2016dcg
sets
functions
0
votes
0
answers
21
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
(
17.6k
points)

18
views
isi2016dcg
sets
0
votes
1
answer
22
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
(
17.6k
points)

21
views
isi2016dcg
sets
functions
0
votes
0
answers
23
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
(
17.6k
points)

16
views
isi2016dcg
sets
functions
+1
vote
1
answer
24
ISI2016DCG50
The domain of the function $\ln(3x^{2}4x+5)$ is set of positive real numbers set of real numbers set of negative real numbers set of real numbers larger than $5$
asked
Sep 18, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.6k
points)

29
views
isi2016dcg
functions
0
votes
1
answer
25
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
(
17.6k
points)

20
views
isi2017dcg
sets
+1
vote
1
answer
26
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
(
17.6k
points)

40
views
isi2018dcg
sets
+1
vote
2
answers
27
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
(
17.6k
points)

58
views
isi2018dcg
sets
+7
votes
3
answers
28
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
asked
Jul 2, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
434k
points)

853
views
ugcnetjune2019ii
poset
settheory&algebra
+1
vote
2
answers
29
UGCNETJune2019II9
Find the zeroone matrix of the transitive closure of the relation given by the matrix $A$ : $A =\begin{bmatrix} 1 & 0& 1\\ 0 & 1 & 0\\ 1& 1& 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 1& 1\\ 0 & 1 & 0\\ 1& 0& 1 \end{bmatrix}$
asked
Jul 2, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
434k
points)

460
views
ugcnetjune2019ii
settheory&algebra
+3
votes
1
answer
30
UGCNETJune2019II13
How many different Boolean functions of degree $n$ are the $2^{2^n}$ $(2^2)^n$ $2^{2^n} 1$ $2^n$
asked
Jul 2, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
434k
points)

213
views
ugcnetjune2019ii
boolean
function
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