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Recent questions and answers in Set Theory & Algebra
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PGEE 2018
If root of equation f(x) is 0 ar x= 3 and X= 3 then root of equation f(x+3) will be at ? A) X= 0 and X=6 B) X=3 and X=3 C) X=6 and X=0; D) X=6 and X= 6
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Set Theory & Algebra
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Akhilesh Singla
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iiithpgee
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2
PGEE 2018
Consider function f: N $\rightarrow$ N, where N is a natural number, which of the following function is not one to one but onto A) f(1)=f(2)=1 f(n)=n1 B) 2n C) $n^{2}$
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8 hours
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Set Theory & Algebra
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abhishekmehta4u
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28
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iiithpgee
functions
+4
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2
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3
ISRODEC20179
The function $f:[0,3]\rightarrow [1,29]$ defined by $f(x)=2x^{3}15x^{2}+36x+1$ is injective and surjective surjective but not injective injective but not surjective neither injective nor surjective
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Set Theory & Algebra
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abhishekmehta4u
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isrodec2017
+1
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1
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4
Set system and linear algebra
We have $m$ sets $A_1,A_2,A_3 \text{ to } A_m$. All $A_i \subseteq [n]$ where $ [n] = \{1,2,3, \dots n \}.$ Given that $A_i = \text{odd number}$ and $A_i \cap A_j = \text{even number }\forall i \neq j$. Show that $m \leq n$.
answered
2 days
ago
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Set Theory & Algebra
by
Sachin Mittal 1
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15.5k
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134
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sets
linearalgebra
+7
votes
6
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5
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
answered
Apr 13
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Set Theory & Algebra
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pankaj_vir
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gate2018
generatingfunctions
normal
0
votes
1
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6
Minus Operation
State true or false? {1,2}  {1,2,3} = ɸ
answered
Apr 13
in
Set Theory & Algebra
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sonveer tomar 1
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891
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40
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+38
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6
answers
7
GATE20151_39
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 $\left\{ \textit{g}\right\}$ are ... Only $\left\{ \textit{g}\right\}$ is functionally complete Neither $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete
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Apr 8
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Set Theory & Algebra
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mehul vaidya
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593
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4.6k
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gate20151
settheory&algebra
functions
difficult
+32
votes
5
answers
8
GATE2014150
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
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Apr 7
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Set Theory & Algebra
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mehul vaidya
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593
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2.4k
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gate20141
settheory&algebra
functions
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numericalanswers
0
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1
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9
Relations
For a set of n elements, what is the number of relations possible if: 1. Relation is neither Reflexive nor Irreflexive 2. Relation is Reflexive, Symmetric but not AntiSymmetric.
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Apr 3
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Set Theory & Algebra
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Deepakk Poonia (Dee)
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47
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3
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10
Difference between Anti and Asymmetric?
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Mar 31
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Set Theory & Algebra
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abhishekmehta4u
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9.7k
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82
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discretemathematics
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+2
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1
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11
Function
answered
Mar 25
in
Set Theory & Algebra
by
abhishekmehta4u
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9.7k
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34
views
functions
discretemathematics
+12
votes
3
answers
12
GATE1998_2.3
The binary relation $R = \{(1, 1), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)\}$ on the set $A=\{1, 2, 3, 4\}$ is reflective, symmetric and transitive neither reflective, nor irreflexive but transitive irreflexive, symmetric and transitive irreflexive and antisymmetric
answered
Mar 24
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Set Theory & Algebra
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abhishekmehta4u
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741
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gate1998
settheory&algebra
easy
relations
0
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1
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13
test series
can somebody explain solution to recurrence relation
answered
Mar 24
in
Set Theory & Algebra
by
pankaj_vir
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6.3k
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43
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+1
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0
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14
discrte
Let A=Z and Let R={(a,b)A x A ;a=r(mod2) and b=r(mod2) Show that R is an equivalence relation.
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Mar 22
in
Set Theory & Algebra
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Amit puri
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29
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0
votes
1
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15
Test series
Let $Z_{24}$ be the set of integers under the addition modulo $24$. $Z_{24} = {0,1, 2,…23}$ Given $6$element subgroup of $Z_{24}$ as $H = {4, 8, 12, 16, 20, 0}$. Find the number of distinct left cosets of $H$. $5$ $6$ $4$ $9$ I understand the meaning of left coset and right coset. Please help me solve this question.
answered
Mar 22
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Set Theory & Algebra
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abhishekmehta4u
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41
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grouptheory
settheory&algebra
+2
votes
1
answer
16
Kenneth Rosen: Lattices
How is this a lattice?
answered
Mar 19
in
Set Theory & Algebra
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abhishekmehta4u
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9.7k
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83
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kennethrosen
discretemathematics
lattice
0
votes
1
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17
Boolean algebra theorem(Lattices)
THEOREM: The Poset $[D_{n};/] $ is a boolean algebra iff 'n' is a squarefree number. If the Poset $[D_{n};/] $ is a boolean algebra then compliment of $x = \frac{n}{x} \forall x\epsilon D_{n}$ Please explain this theorem?? and following question Q)Which of the following is not a ... A) [ D_{110};/ ] $ $ B) [ D_{91};/ ] $ $ C) [ D_{45};/ ]$ $ D) [ D_{64};/ ]$
answered
Mar 19
in
Set Theory & Algebra
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abhishekmehta4u
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9.7k
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88
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discretemathematics
lattice
booleanalgebra
0
votes
2
answers
18
Distributive lattice
Q)which of the following is not a distributive lattice? a) [P(A);$\preceq$ ] where A = { a,b,c,d } b) [ {1,2,3,5,30} ; / ]
answered
Mar 17
in
Set Theory & Algebra
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Ananya Jaiswal 1
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1.2k
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75
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discretemathematics
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lattice
0
votes
1
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19
MCQs in Computer Science  Timothy Williams
answered
Mar 12
in
Set Theory & Algebra
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Deepakk Poonia (Dee)
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2.9k
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69
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discretemathematics
discrete
settheory&algebra
+2
votes
1
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20
Self doubt Set
True/False $\left \{ \phi \right \} \neq \phi$
answered
Mar 12
in
Set Theory & Algebra
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Deepakk Poonia (Dee)
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2.9k
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59
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discretemathematics
+1
vote
1
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21
Set theory
Consider a set S $\left \{ 2,3,4,.....,23,24 \right \}$ and R is relation on S such that aRb if a divides b, then find the number of minimal elements in its hasse diagram
answered
Mar 11
in
Set Theory & Algebra
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Deepakk Poonia (Dee)
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102
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discretemathematics
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relations
+1
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1
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22
Equivalence relation
Q)Which of the following is not an equivalence relation on a set of all real numbers? A) R1 = { (a,b) / ab is a integer } B) R2 = { (a,b) / ab is divisible by 5 } C) R3 = { (a,b) / ab is an odd number } D) R4 = { (a,b) / ab is an even number }
answered
Mar 11
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Set Theory & Algebra
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abhishekmehta4u
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discretemathematics
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equivalence
relations
+16
votes
3
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23
GATE20022.17
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetric Symmetric and reflexive Transitive and reflexive Transitive and symmetric
answered
Mar 10
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Set Theory & Algebra
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Mk Utkarsh
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11.9k
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1.5k
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gate2002
settheory&algebra
normal
relations
0
votes
1
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24
Group theory
Let $G$ be a finite group with sub group $H$ & $K$ such that $H=7$ and $K=31$ then find $ H ⋂ K$
answered
Mar 8
in
Set Theory & Algebra
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Sukanya Das
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11.2k
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62
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engineeringmathematics
settheory&algebra
sets
+1
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1
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25
Gate CSE Web Link on Groups: Conceptual Doubt
answered
Mar 6
in
Set Theory & Algebra
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bhargav50
(
53
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70
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groups
+3
votes
1
answer
26
ISRODEC20174
If $x=1$ and $x=2$ are extreme points of $f(x)=\alpha \log \mid x \mid+\beta x^2+x$ then $\alpha=6,\beta=\dfrac{1}{2}$ $\alpha=2,\beta=\dfrac{1}{2}$ $\alpha=2,\beta=\dfrac{1}{2}$ $\alpha=6,\beta=\dfrac{1}{2}$
answered
Mar 4
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Set Theory & Algebra
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Amit puri
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754
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isrodec2017
+1
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1
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27
TEST SERIES
A binary relation R on Z × Z is deﬁned as follows: ( a , b ) R ( c , d ) iff a = c or b = d Consider the following propositions: 1. R is reflexive.2. R is symmetric. 3. R is antisymmetric. Which one of the following statements are True?
answered
Mar 3
in
Set Theory & Algebra
by
Mk Utkarsh
Boss
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11.9k
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67
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+1
vote
2
answers
28
Kenneth Rosen Edition7 Ch1 Ex1.2 QueNo5
answered
Mar 1
in
Set Theory & Algebra
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Pham Khanh
(
17
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212
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kennethrosen
descriptive
settheory&algebra
+2
votes
1
answer
29
Check which one is this
The binary operation defined on a,b∈z such that a*b= min(a,b)then (A,*) is a)monoid b)group c)algebricstructure d)semi group
answered
Feb 25
in
Set Theory & Algebra
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Mk Utkarsh
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11.9k
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96
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discretemathematics
groups
+1
vote
2
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30
Maths: Group Theory
Que: Which one of the following is not true? a) In a group (G,*), if a*a = a, then a=e, where e is an identity element. b) In a group (G,*), if x1 = x, ∀x ∈ G, then G is an Abelian group. c) In a group (G,*), if (a*b)2 = (a2*b2) then G is an Abelian group. ... (G,*), if (a*b)n = (an*bn) then G is an Abelian group, where n={2, 3, 4, ......} PS: c) and d) seem correct to me.
answered
Feb 25
in
Set Theory & Algebra
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Mk Utkarsh
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11.9k
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185
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discretemathematics
groups
abeliangroup
settheory&algebra
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31
Generating Function
How to apply this theorem to $\frac{x^{3}}{1x}$
answered
Feb 24
in
Set Theory & Algebra
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Lakshman Patel RJIT
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7.5k
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89
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generatingfunctions
discretemathematics
+2
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1
answer
32
ISI2011A3b
The numbers 1, 2, . . . , 10 are arranged in a circle in some order. Show that it is always possible to find three adjacent numbers whose sum is at least 17, irrespective of the ordering.
answered
Feb 20
in
Set Theory & Algebra
by
Mk Utkarsh
Boss
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11.9k
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107
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descriptive
isi2011
pigeonhole
+8
votes
3
answers
33
GATE201827
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
answered
Feb 19
in
Set Theory & Algebra
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Neelay Upadhyaya
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935
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1.5k
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gate2018
settheory&algebra
#countableset
normal
0
votes
1
answer
34
NIELIT ScientistB Dec 2017_24
Using bisection method, one root of X4X1 lies between 1 and 2. After second iteration the root may lie in interval : (A) (1.25, 1.5) (B) (1, 1.25) (C) (1, 1.5) (D) None of the options
answered
Feb 18
in
Set Theory & Algebra
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Manohar Kumar Sing 1
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11
points)

123
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+1
vote
1
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35
Distributed Lattice
Is the following lattice distributed ?
answered
Feb 18
in
Set Theory & Algebra
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Mk Utkarsh
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11.9k
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128
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lattice
settheory&algebra
+1
vote
1
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36
isro exam december 2017
The number of elements in the power set of {{1,2},{2,1,1},{2,1,1,2}} is:
answered
Feb 18
in
Set Theory & Algebra
by
saket nandan
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429
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isro2017
0
votes
1
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37
how to solve
answered
Feb 16
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Set Theory & Algebra
by
Tesla!
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15.4k
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86
views
+3
votes
4
answers
38
GATE201819
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
answered
Feb 14
in
Set Theory & Algebra
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RFITNES. TK
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357
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1.5k
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gate2018
groups
numericalanswers
0
votes
0
answers
39
Closure of Relations
Let R be a relation on a set A. R may or may not have some property P, such as reflexivity, symmetry, or transitivity. If there is a relation S with property P containing R such that S is a subset of every relation with property P containing R, then S is called the closure Relations of R with respect to P. can someone explain this definition in simple words?
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Feb 14
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Set Theory & Algebra
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Mk Utkarsh
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11.9k
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41
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discretemathematics
kennethrosen
settheory&algebra
closureproperty
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1
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40
Composition of functions
There exist 3 sets(A,B,C) and 2 functions f and g. g be a function from set A to set B f be a function from set B to set C then composition of both the functions is denoted by $f \circ g$ which exists. Then what is the necessary condition for the following 2 functions for the existence of $g \circ f$ a) Injection b) Surjection c) Bijection d) None of these
answered
Feb 13
in
Set Theory & Algebra
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shashanksingh
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231
points)

112
views
discretemathematics
functions
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