Recent questions tagged set-theory&algebra / GATE Overflow for GATE CSE

1 votes

2 answers

1021

What are the generators for the group G having multiplication modulo 6 as an operation?
What are the generators for the group G={1,2,3,4,5,6} having multiplication modulo 6 as an operation?

What are the generators for the group G={1,2,3,4,5,6} having multiplication modulo 6 as an operation?

Nilam

3.4k views

Nilam asked Oct 19, 2015

21 votes

3 answers

1022

TIFR CSE 2011 | Part A | Question: 10
Let $m$, $n$ denote two integers from the set $\{1, 2,\dots,10\}$. The number of ordered pairs $\left ( m, n \right )$ such that $2^{m}+2^{n}$ is divisible by $5$ is. $10$ $14$ $24$ $8$ None of the above

Let $m$, $n$ denote two integers from the set $\{1, 2,\dots,10\}$. The number of ordered pairs $\left ( m, n \right )$ such that $2^{m}+2^{n}$ is divisible by $5$ is.$10$...

makhdoom ghaya

2.0k views

makhdoom ghaya asked Oct 17, 2015

3 votes

1 answer

1023

TIFR2010-Maths-B-9
Let $G=\left \{ z \in \mathbb{C} \mid z^n = 1 \text{ for some positive integer } n \right \}$. Then under multiplication of complex numbers, $G$ is a group of finite order $G$ is a group of infinite order, but every element of $G$ has finite order $G$ is a cyclic group None of the above

Let $$G=\left \{ z \in \mathbb{C} \mid z^n = 1 \text{ for some positive integer } n \right \}$$. Then under multiplication of complex numbers,$G$ is a group of finite ord...

makhdoom ghaya

1.7k views

makhdoom ghaya asked Oct 12, 2015

3 votes

3 answers

1024

TIFR2010-Maths-B-6
Let $A, B$ be subsets of $\mathbb{R}$. Define $A + B$ to be the set of all sums $x +y$ with $x \in A$ and $y \in B$. Which of the following statements is false? If $A$ and $B$ are bounded, then $A + B$ is bounded If $A$ and $B$ are open, then $A + B$ is open If $A$ and $B$ are closed, then $A + B$ is closed If $A$ and $B$ are connected, then $A + B$ is connected

Let $A, B$ be subsets of $\mathbb{R}$. Define $A + B$ to be the set of all sums $x +y$ with $x \in A$ and $y \in B$. Which of the following statements is false?If $A$ and...

makhdoom ghaya

952 views

makhdoom ghaya asked Oct 12, 2015

3 votes

1 answer

1025

TIFR2010-Maths-B-3
If $f,g:\mathbb{R}\rightarrow \mathbb{R}$ are uniformly continuous functions, then their compositions g ∘ f is. Uniformly continuous Continuous but not uniformly continuous Continuous and bounded None of the above

If $f,g:\mathbb{R}\rightarrow \mathbb{R}$ are uniformly continuous functions, then their compositions g ∘ f is.Uniformly continuousContinuous but not uniformly continuo...

makhdoom ghaya

1.4k views

makhdoom ghaya asked Oct 11, 2015

5 votes

1 answer

1026

TIFR2010-Maths-A-9
The total number of subsets of a set of 6 elements is. 720 $6^{6}$ 21 None of the above

The total number of subsets of a set of 6 elements is.720$6^{6}$21None of the above

makhdoom ghaya

1.2k views

makhdoom ghaya asked Oct 11, 2015

4 votes

2 answers

1027

TIFR2010-Maths-A-5
Let $f$ be an one to one function from the closed interval [0, 1] to the set of real numbers $R$, then. $f$ must be onto Range of $f$ must contain a rational number Range of $f$ must contain an irrational number Range of $f$ must contain both rational and irrational numbers

Let $f$ be an one to one function from the closed interval [0, 1] to the set of real numbers $R$, then.$f$ must be ontoRange of $f$ must contain a rational numberRange of...

makhdoom ghaya

3.0k views

makhdoom ghaya asked Oct 11, 2015

4 votes

1 answer

1028

TIFR2010-Maths-A-2
Which of the following is false? Any abelian group of order 27 is cyclic Any abelian group of order 14 is cyclic Any abelian group of order 21 is cyclic Any abelian group of order 30 is cyclic

Which of the following is false?Any abelian group of order 27 is cyclicAny abelian group of order 14 is cyclicAny abelian group of order 21 is cyclicAny abelian group of ...

makhdoom ghaya

2.3k views

makhdoom ghaya asked Oct 11, 2015

4 votes

4 answers

1029

How many number of possible relations in a antisymmetric set?
I just want to know how the value in the answers come like 2^n2 and 2^n^2-1 etc. Please make it clear.

I just want to know how the value in the answers come like 2^n2 and 2^n^2-1 etc. Please make it clear.

admin

5.4k views

admin asked Oct 9, 2015

4 votes

1 answer

1030

how many subsets does P(A) have if A is null set?
let A={} or phi be null set.it has 0 elements and 1 subset that is itself. P(A) represents power set of A.how many elements and subsets does P(A) has? i think P(A)={ {} } has 1 element ie {}..now P(A) should have 2 ... set containing null set) so P(A) should have 1 element and 2 subsets..at lot of places ans is given as 1 subset so please clarify?

let A={} or phi be null set.it has 0 elements and 1 subset that is itself.P(A) represents power set of A.how many elements and subsets does P(A) has? i think P(A)={ {} } ...

Anurag_s

4.6k views

Anurag_s asked Oct 5, 2015

10 votes

3 answers

1031

TIFR CSE 2010 | Part A | Question: 15
Let $A, B$ be sets. Let $\bar{A}$ denote the complement of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are not in $B$. Set $(A - (A - B))$ is equal to: $B$ $A\cap \bar{B}$ $A - B$ $A\cap B$ $\bar{B}$

Let $A, B$ be sets. Let $\bar{A}$ denote the complement of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are not i...

makhdoom ghaya

1.5k views

makhdoom ghaya asked Oct 3, 2015

2 votes

1 answer

1032

If f:X→Y and a, b⊆X, then
If $f:X→Y$ and $a, b \subseteq X$, then $f(a \cap b)$ is equal to $f(a) –f(b)$ $f(a) \cap f(b)$ a proper subset of $f(a)\cap f(b)$ $f(b)–f(a)$

If $f:X→Y$ and $a, b \subseteq X$, then$f(a \cap b)$ is equal to$f(a) –f(b)$$f(a) \cap f(b)$a proper subset of $f(a)\cap f(b)$$f(b)–f(a)$

Tendua

6.7k views

Tendua asked Sep 29, 2015

0 votes

1 answer

1033

If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is R composite R?

If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is Rcomposite R?(a) ((1,1), (3, 1), (2, 3), (4, 2))(b) ((1, 1), (9, 1), (4, 9...

Tendua

10.3k views

Tendua asked Sep 24, 2015

2 votes

2 answers

1034

Determine the cardinality of the following set
Determine the cardinality of the following set: $\{x \mid x\text{ is an integer and } 1/8 < x < 17/2\}$

Determine the cardinality of the following set:$$\{x \mid x\text{ is an integer and } 1/8 < x < 17/2\}$$

gate#2016

904 views

gate#2016 asked Jul 28, 2015

2 votes

1 answer

1035

set theory
difference between {} , ∅ , {∅} ???

difference between {} , ∅ , {∅} ???

focus _GATE

841 views

focus _GATE asked Jul 16, 2015

1 votes

3 answers

1036

What is the difference between diagonal relation and reflexive relation?

gate#2016

2.2k views

gate#2016 asked Jul 10, 2015

0 votes

1 answer

1037

Please explain
What is a Toset? It is poset+all elements should be comparable. What does comparable mean (C,<=) is a toset how? Complex numbers are not comparable nless in a+ib c+id it is mentioned whether a<c etc.But if they are not comparable,then how can one say c1 <=c2 implies c2<=c1 do not exist.(Since it is a poset ,anti symmetricity should hold)

What is a Toset? It is poset+all elements should be comparable.What does comparable mean(C,<=) is a toset how?Complex numbers are not comparable nless in a+ib c+id it is ...

Jarvis

479 views

Jarvis asked Jul 8, 2015

0 votes

2 answers

1038

Can you please help me understand Antisymmetric relation
Hi , I am stuck with Antisymmetric relations. I know the formal definition . If A = {a,b} , If aRb ^ bRa both true then a=b for all a,b belongs to A. Now , while the formal definition is ok , for practical purpose I found out that diagonal ... and (c,c) is diagonal element ) But , I can not understand how {(a,b) , (c,b)} is anti-symmetric .

Hi ,I am stuck with Antisymmetric relations. I know the formal definition . If A = {a,b} , If aRb ^ bRa both true then a=b for all a,b belongs to A.Now , while the forma...

worst_engineer

688 views

worst_engineer asked Jul 3, 2015

1 votes

2 answers

1039

f:R->R be such that f(x)=x^3-3x^2+5x -10..prove that whether it is one to one or onto or both..
please give me adetail solution.basically I am getting confused how to determine onto function or not for a polynomial.please answer me as early as possible..

please give me adetail solution.basically I am getting confused how to determine onto function or not for a polynomial.please answer me as early as possible..

resuscitate

7.2k views

resuscitate asked May 1, 2015

43 votes

7 answers

1040

GATE CSE 2015 Set 3 | Question: 41
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about $R$? Both reflexive and symmetric Reflexive but not symmetric Not reflexive but symmetric Neither reflexive nor symmetric

Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about ...

go_editor

12.9k views

go_editor asked Feb 15, 2015

52 votes

3 answers

1041

GATE CSE 2015 Set 3 | Question: 23
Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T$. For any $T, R \in U \text{ let } T \backslash R$ be the set ... $X \backslash Y = \phi)$ $\forall X \in U, \forall Y \in U, (X \backslash Y = Y' \backslash X')$

Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T...

go_editor

12.0k views

go_editor asked Feb 14, 2015

30 votes

3 answers

1042

GATE CSE 2015 Set 3 | Question: 2
Let $\#$ be the binary operator defined as $X\#Y = X'+Y'$ where $X$ and $Y$ are Boolean variables. Consider the following two statements. $(S_1)$ $(P\#Q)\#R = P\#(Q\#R)$ $(S_2)$ $Q\#R = (R\#Q)$ Which are the following is/are true for the ... $R$? Only $S_1$ is true Only $S_2$ is true Both $S_1$ and $S_2$ are true Neither $S_1$ nor $S_2$ are true

Let $\#$ be the binary operator defined as$X\#Y = X'+Y'$ where $X$ and $Y$ are Boolean variables.Consider the following two statements.$(S_1)$ $(P\#Q)\#R = P\#(Q\#R)$$(S_...

go_editor

5.6k views

go_editor asked Feb 14, 2015

77 votes

6 answers

1043

GATE CSE 2015 Set 1 | Question: 34
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram: For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \wedge y$ are join and meet of $x, y$ ... $p_r = 0$ $p_r = 1$ $0 < p_r ≤ \frac{1}{5}$ $\frac{1}{5} < p_r < 1$

Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram:For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \we...

makhdoom ghaya

17.3k views

makhdoom ghaya asked Feb 13, 2015

38 votes

5 answers

1044

GATE CSE 2015 Set 2 | Question: 54
Let $X$ and $Y$ denote the sets containing $2$ and $20$ distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being one-to-one is ______.

Let $X$ and $Y$ denote the sets containing $2$ and $20$ distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be...

go_editor

8.3k views

go_editor asked Feb 13, 2015

66 votes

6 answers

1045

GATE CSE 2015 Set 1 | Question: 1‏6
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\varnothing \in 2^{A}$ $\varnothing \subseteq 2^{A}$ ... I and III only II and III only I, II and III only I, II and IV only

For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE?$\varnoth...

makhdoom ghaya

15.5k views

makhdoom ghaya asked Feb 13, 2015

25 votes

2 answers

1046

GATE CSE 2015 Set 1 | Question: 28
The binary operator $\neq$ ... about the binary operator $\neq$ ? Both commutative and associative Commutative but not associative Not commutative but associative Neither commutative nor associative

The binary operator $\neq$ is defined by the following truth table.$$\begin{array}{|l|l|l|} \hline \textbf{p} & \textbf{q}& \textbf{p} \neq \textbf{q}\\\hline \text{0} & ...

makhdoom ghaya

6.4k views

makhdoom ghaya asked Feb 13, 2015

52 votes

15 answers

1047

GATE CSE 2015 Set 2 | Question: 40
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.

The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.

go_editor

19.5k views

go_editor asked Feb 12, 2015

23 votes

6 answers

1048

GATE CSE 2015 Set 2 | Question: 18
The cardinality of the power set of $\{0, 1, 2, \dots , 10\}$ is _______

The cardinality of the power set of $\{0, 1, 2, \dots , 10\}$ is _______

go_editor

5.2k views

go_editor asked Feb 12, 2015

38 votes

2 answers

1049

GATE CSE 2015 Set 2 | Question: 16
Let $R$ be the relation on the set of positive integers such that $aRb$ and only if $a$ and $b$ are distinct and let have a common divisor other than $1.$ Which one of the following statements about $R$ is true? $R$ is ... but not symmetric not transitive $R$ is transitive but not reflexive and not symmetric $R$ is symmetric but not reflexive and not transitive

Let $R$ be the relation on the set of positive integers such that $aRb$ and only if $a$ and $b$ are distinct and let have a common divisor other than $1.$ Which one of th...

go_editor

7.7k views

go_editor asked Feb 12, 2015

18 votes

2 answers

1050

GATE CSE 2015 Set 2 | Question: 9
The number of divisors of $2100$ is ____.

The number of divisors of $2100$ is ____.

go_editor

9.0k views

go_editor asked Feb 12, 2015

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