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Recent questions and answers in Set Theory & Algebra
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#self doubt
How to solve it?
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Ace booklet questions no 07
If A∆B = (A intersection B) whole complement than the universal set is??
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acebooklet
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Group theory
In theorem 1: It is said that group is abelian if and only if order of group is prime number In theorem 2 : It is said that the group having order as square of prime number is abelian Theorem 1: https://yutsumura.com/asimpleabeliangroupifandonlyifthe ... The group is not abelian as order is not prime. Theorem 2: 4 = (2)^2 square of prime number hence abelian. Please clarify ..
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2
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GATE20131
A binary operation $\oplus$ on a set of integers is defined as $x \oplus y = x^{2}+y^{2}$. Which one of the following statements is TRUE about $\oplus$? Commutative but not associative Both commutative and associative Associative but not commutative Neither commutative nor associative
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3 days
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Set Theory & Algebra
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Raghava45
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1.2k
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gate2013
settheory&algebra
easy
binaryoperation
+18
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6
answers
5
GATE200543
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto
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4 days
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gate2005
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6
Group theory
Which of the following operation on A is closed; where set A={0,1,2,3,4,5,6,7}? a) a*b=abmod10 b)a*b=abmod10 c) a*b=(a^2 + 2ab + b^2) mod 10 d) a*b=(7a+b) mod 10
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5 days
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11
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7
#self doubt
https://gateoverflow.in/214013/isi2017mma28 give me the solution of this question by using example only.not able to understand explanation.
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Shubham Aggarwal
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8
Countable and Uncountable Self Doubt 2
Which of the following is always correct? A. Cross product of two countable set is countable B. Cross product of two countable set is uncountable C. Cross product of two uncountable set is countable D. Cross product of uncountable ... E. Cross product of uncountable and countable set is countable F. Cross product of uncountable and countable set is uncountable
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Sep 11
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smsubham
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theoryofcomputation
#countableset
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Countable and uncountable Self Doubt 1
which of the following is always correct? A. Union of two uncountable set is uncountable B. The intersection of two uncountable set is uncountable C. Union of two uncountable set is countable D. The intersection of two uncountable set is ... is countable I. The complement of a countable set is countable. J. The complement of a countable set is uncountable.
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Sep 11
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smsubham
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#countableset
theoryofcomputation
settheory&algebra
+9
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5
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10
GATE199115,a
Show that the product of the least common multiple and the greatest common divisor of two positive integers $a$ and $b$ is $a\times b$.
answered
Sep 8
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Set Theory & Algebra
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Sourav Basu
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447
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gate1991
settheory&algebra
normal
numbertheory
proof
descriptive
+17
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5
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11
GATE200424
Consider the binary relation: $S= \left\{\left(x, y\right) \mid y=x+1 \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$ The reflexive transitive closure is $S$ is $\left\{\left(x, y\right) \mid y >x \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$ $\left ... , 2\right\} \right\}$ $\left\{\left(x, y\right) \mid y \leq x \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$
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Sep 8
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Sourav Basu
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gate2004
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relations
+2
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1
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12
Topological ordering in Hasse diagram
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Sep 7
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nooftopologicalordering
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Why is composition of functions unequal in below question ?
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Sep 7
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radha gogia
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functions
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UGCNETDec2009ii01
If she is my friend and you are her friend, then we are friends. Given this, the friend relationship in this context is ____________. (i) commutative (ii) transitive (iii) implicative (iv) equivalence (A) (i) and (ii) (B) (iii) (C) (i), (ii), (iii) and (iv) (D) None of these
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Sep 6
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ugcnetdec2009ii
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Test Series
Is 1 a lattice?
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Sep 6
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Vineet Kumar 1
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lattice
partialorder
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16
Kenneth Rosen Section 9.5 Exercise problem #3.e
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Sep 4
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Abhijit Sen 4
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249
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30
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discretemathematics
kennethrosen
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1
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17
Function
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Sep 3
in
Set Theory & Algebra
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sidlewis
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327
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22
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+17
votes
5
answers
18
GATE2005IT33
Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $S_2\subset S_1$. What is the maximum cardinality of C? $n$ $n+1$ $2^{n1} + 1$ $n!$
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Sep 1
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Set Theory & Algebra
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Sourav Basu
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gate2005it
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19
Set Theory
Answer given is A.Is it correct?
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Sep 1
in
Set Theory & Algebra
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Shaik Masthan
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29
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0
votes
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20
Dual of a lattice
What is dual of a lattice? Also give an example
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Aug 31
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sakharam
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lattice
+20
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3
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21
GATE2006IT6
Given a boolean function $f (x_1, x_2, \ldots, x_n),$ which of the following equations is NOT true? $f (x_1, x_2, \ldots, x_n) = x_1'f(x_1, x_2, \ldots, x_n) + x_1f(x_1, x_2, \ldots, x_n)$ $f (x_1, x_2, \ldots, x_n) = x_2f(x_1, x_2, \ldots , x_n) + x_2'f(x_1, x_2, \ldots ... , 0) + x_nf(x_1, x_2, \ldots,1)$ $f (x_1, x_2, \ldots , x_n) = f(0, x_2, , x_n) + f(1, x_2, \ldots, x_n)$
answered
Aug 31
in
Set Theory & Algebra
by
skeltro
(
81
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890
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gate2006it
settheory&algebra
functions
normal
+11
votes
2
answers
22
GATE199812
Let $(A, *)$ be a semigroup, Furthermore, for every $a$ and $b$ in $A$, if $a \neq b$, then $a*b \neq b*a$. Show that for every $a$ in $A$, $a*a=a$ Show that for every $a$, $b$ in $A$, $a*b*a=a$ Show that for every $a,b,c$ in $A$, $a*b*c=a*c$
answered
Aug 29
in
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Sourav Basu
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766
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gate1998
settheory&algebra
groups
descriptive
0
votes
2
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23
self doubt
What will be lower bound of {g}
answered
Aug 28
in
Set Theory & Algebra
by
aditi19
Junior
(
647
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25
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lattice
discretemathematics
engineeringmathematics
0
votes
0
answers
24
Function Mapping
In a function if X and Y two sets "All element of X need to be mapped, but all element of Y neednot to be mapped " So, answer here will be A) or D)? https://gateoverflow.in/2707/gate199613
[closed]
asked
Aug 27
in
Set Theory & Algebra
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srestha
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95.5k
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13
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discretemathematics
0
votes
0
answers
25
Functions
1)How many injective function are there which are also bijective with n elements? 2)How many injective function of n elements are there among which m elements are also bijective ? 3)How many onto function of n elements are there among which m elements are also bijective ? 4)How many injective function of n elements are there among which m elements are also surjective ?
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Aug 27
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Set Theory & Algebra
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srestha
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15
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discretemathematics
functions
0
votes
0
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26
SELF DOUBT REGARDING SYLLABUS
https://gateoverflow.in/80586/gate19872f IS THERE NEED TO KNOW POOF ?IF YES THEN GIVE ANY EASY PROOF...
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Aug 27
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eyeamgj
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+24
votes
4
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27
GATE200337
Let \(f : A \to B\) be an injective (onetoone) function. Define \(g : 2^A \to 2^B\) as: \(g(C) = \left \{f(x) \mid x \in C\right\} \), for all subsets $C$ of $A$. Define \(h : 2^B \to 2^A\) as: \(h(D) = \{x \mid x \in A, f(x) \in D\}\), for all subsets $D$ of ... always true? \(g(h(D)) \subseteq D\) \(g(h(D)) \supseteq D\) \(g(h(D)) \cap D = \phi\) \(g(h(D)) \cap (B  D) \ne \phi\)
answered
Aug 24
in
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Sourav Basu
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1.6k
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gate2003
settheory&algebra
functions
normal
+11
votes
4
answers
28
GATE19981.7
Let $R_1$ and $R_2$ be two equivalence relations on a set. Consider the following assertions: $R_1 \cup R_2$ is an equivalence relation $R_1 \cap R_2$ is an equivalence relation Which of the following is correct? Both assertions are true Assertions (i) is true but assertions (ii) is not true Assertions (ii) is true but assertions (i) is not true Neither (i) nor (ii) is true
answered
Aug 24
in
Set Theory & Algebra
by
superak96
(
37
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1.7k
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gate1998
settheory&algebra
relations
normal
+4
votes
3
answers
29
ISI2016
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
answered
Aug 23
in
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sutanay3
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2.6k
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324
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isi2016
settheory&algebra
numbertheory
numericalanswers
+16
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4
answers
30
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
Aug 22
in
Set Theory & Algebra
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superak96
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37
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1.8k
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gate2002
settheory&algebra
normal
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0
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1
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31
Relations
What is the smallest binary relation possible from A to B? Is it Null Set? If so, how is it possible relations are subsets of AxB (cartesian product) and if AxB is not supposed to be containing a Null Set.
answered
Aug 22
in
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Lakshay Kakkar
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16
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sets
relations
discretemathematics
0
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32
Descrete maths
$\text{Prove that : the union of any two subgroup of 'G' is not subgroup of 'G'}$ $\text{Prove that : the intersection of any two subgroup of 'G' is also a subgroup of 'G'}$
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Aug 22
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Prince Sindhiya
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10
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zeal
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1
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33
Self doubt
Let (g,*) be a group of order p where p is a prime number then number of proper subgroup is? I am getting 1 that is identity element, but somewhere I read, it will be 0. Who is wrong?
answered
Aug 20
in
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by
Tesla!
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(
16.5k
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15
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discretemathematics
+12
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4
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34
GATE2008IT28
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only
answered
Aug 20
in
Set Theory & Algebra
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sutanay3
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gate2008it
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lattice
normal
0
votes
2
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35
Sets and relations
If A is a set of positive odd elements less than 10. Then what is the cardinality of set A?
answered
Aug 19
in
Set Theory & Algebra
by
aditi19
Junior
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647
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69
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permutationsandcombinations
settheory&algebra
+5
votes
2
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36
ISI2004MIII
The equation $\frac{1}{3}+\frac{1}{2}s^{2}+\frac{1}{6}s^{3}=s$ has exactly three solution in $[0.1]$ exactly one solution in $[0,1]$ exactly two solution in $[0,1]$ no solution in $[0,1]$
answered
Aug 19
in
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sutanay3
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isi2004
polynomials
0
votes
1
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37
Types of Functions
A and B are finite sets True or False 1) F:A>B is one to one then F is Onto , where A = B 2) F:A>A is one to one then F is Onto , where F is function on same set
answered
Aug 19
in
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Rishav Kumar Singh
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0
votes
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38
Countability and Well Ordering
Is there any relation between countability and well ordering? I mean if a set is well ordered, does it have any influence on it being countable and vice versa?
asked
Aug 19
in
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Lakshay Kakkar
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#countableset
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1
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39
State True/False
1. If f is bijective function then f1 is also bijective function. 2. If f is surjective function then f1 is a function but not surjective. 3. Inverse of a function 'f' is a function only when it is bijective. 4. If a relation R: X>Y is left total, then it must be a function.
answered
Aug 17
in
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shubham6596
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179
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1
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40
TIFR2011MathsA22
There exists a group with a proper subgroup isomorphic to itself.
answered
Aug 17
in
Set Theory & Algebra
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ami
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23
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76
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tifrmaths2011
groups
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