Search results for partial-order / GATE Overflow for GATE CSE

41 votes

3 answers

1

GATE CSE 2007 | Question: 26
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:

Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on$S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overl...

Kathleen

13.4k views

Kathleen asked Sep 21, 2014

42 votes

8 answers

2

GATE CSE 2004 | Question: 73
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$

The inclusion of which of the following sets into$S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3,...

Kathleen

12.9k views

Kathleen asked Sep 18, 2014

58 votes

6 answers

3

GATE CSE 2003 | Question: 31
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S $\to$ {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) $\implies$ P(y) for all $x, y \in S$ satisfying $x \leq y$ ... for all x $\in$ S such that b ≤ x and x ≠ c P(x) = False for all x $\in$ S such that a ≤ x and b ≤ x

Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S $\to$ {True, False} be a predicate defined on S. Suppose that P(...

Kathleen

11.7k views

Kathleen asked Sep 16, 2014

22 votes

5 answers

4

GATE CSE 1996 | Question: 1.2
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is $3$ $4$ $9$ None of the above

Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is$3$$4$$9$No...

Kathleen

13.4k views

Kathleen asked Oct 9, 2014

32 votes

7 answers

5

GATE IT 2007 | Question: 23
A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division. $(0, 0) \in P.$ $(a, b) \in P$ if and only if $(a \% 10) \leq (b \% 10$) and $(\frac{a}{10},\frac{b}{10})\in P.$ ... $P$? (i) and (iii) (ii) and (iv) (i) and (iv) (iii) and (iv)

A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division.$(0, 0) \in P.$$(a, b) \in P$ if and only if $(a \% 1...

Ishrat Jahan

11.4k views

Ishrat Jahan asked Oct 29, 2014

2 votes

2 answers

6

GATE CSE 2024 | Set 2 | Question: 24
Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows \[ P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\} \] The number of total orders on $\{1,2,3,4\}$ that contain $\text{P}$ is __________.

Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows\[P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\}\]The number of total orders ...

Arjun

2.1k views

Arjun asked Feb 16

1 votes

1 answer

7

GO Classes Set Theory And Algebra Practice Set 1 | Question: 10
Are the following relations reflexive, symmetric, transitive, antisymmetric? Explain. Let $R$ be a relation on $\mathbb{Z}$ such that $(a, b) \in R$ iff $b=a$ or $b=-a$. Let $R$ be a relation on $\mathbb{R}$ ... $(a, b) \in R$ iff $a+b$ is a rational number, that is can be represented by a fraction.

Are the following relations reflexive, symmetric, transitive, antisymmetric? Explain.Let $R$ be a relation on $\mathbb{Z}$ such that $(a, b) \in R$ iff $b=a$ or $b=-a$.Le...

GO Classes

295 views

GO Classes asked May 28, 2023

1 votes

1 answer

8

GO Classes Set Theory And Algebra Practice Set 1 | Question: 8
Consider the following binary relations on the naturals (non-negative integers). Which ones are reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify your claims. $A(x, y)$, defined to be true if and only if $y$ ... because eight comes before eighty-one, and $E(8,8)$ is true because eight comes no later than eight.)

Consider the following binary relations on the naturals (non-negative integers). Which ones are reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify ...

GO Classes

382 views

GO Classes asked May 28, 2023

1 votes

1 answer

9

GO Classes Set Theory And Algebra Practice Set 1 | Question: 14
Determine if each of the following relations is reflexive, symmetric, antisymmetric, or transitive. Indicate if the relation is an equivalence relation. $R_1=\{(a, b) \mid-1 \leq a-b \leq 1\}$ on $\mathbf{R}$ ... $\mathbf{N}$ $ R_7=\left\{(a, b) \mid \frac{a}{b} \in \mathbf{Z}\right\}$ on $\mathbf{Z}$

Determine if each of the following relations is reflexive, symmetric, antisymmetric, or transitive. Indicate if the relation is an equivalence relation.$R_1=\{(a, b) \mid...

GO Classes

408 views

GO Classes asked May 28, 2023

1 votes

1 answer

10

GO Classes Set Theory And Algebra Practice Set 1 | Question: 12
Define the binary relation $R$ on the set $A:=\{-4,-3,-2,-1,1,2,3,4\}$ as follows: $ (x, y) \in R \Longleftrightarrow\left|x^2-y^2\right| \leqslant 5 $ for all $x, y \in A$. Which of the following statements ... at all. $R$ is reflexive. $R$ is irreflexive. $R$ is transitive. $R$ is symmetric. $R$ is asymmetric. $R$ is antisymmetric.

Define the binary relation $R$ on the set $A:=\{-4,-3,-2,-1,1,2,3,4\}$ as follows:$$(x, y) \in R \Longleftrightarrow\left|x^2-y^2\right| \leqslant 5$$for all $x, y \in A$...

GO Classes

301 views

GO Classes asked May 28, 2023

1 votes

1 answer

11

GO Classes Set Theory And Algebra Practice Set 1 | Question: 15
Let $R \subseteq \mathbb{N} \times \mathbb{N}$ be a relation ( $a$ binary relation) on the set of natural numbers defined as follows: $ (x, y) \in R \Leftrightarrow x+y \geq 18 \text {. } $ is $R$ reflexive ... . is R symmetric? Prove your answer. Is $R$ antisymmetric? Prove your answer. Is $\mathrm{R}$ transitive? Prove your answer.

Let $R \subseteq \mathbb{N} \times \mathbb{N}$ be a relation ( $a$ binary relation) on the set of natural numbers defined as follows:$$(x, y) \in R \Leftrightarrow x+y \g...

GO Classes

292 views

GO Classes asked May 28, 2023

1 votes

1 answer

12

GO Classes Set Theory And Algebra Practice Set 1 | Question: 13
$ R=\left\{(x, y) \in \mathbb{N}^2: \exists n \in \mathbb{N}, x^n=y\right\} $ is a binary relation on the set of natural numbers $\mathbb{N}$. Determine which of the following properties ... symmetric Transitive For each property, either justify that the property always holds or show by a counterexample that the property does not hold.

$$R=\left\{(x, y) \in \mathbb{N}^2: \exists n \in \mathbb{N}, x^n=y\right\}$$is a binary relation on the set of natural numbers $\mathbb{N}$.Determine which of the follow...

GO Classes

223 views

GO Classes asked May 28, 2023

1 votes

1 answer

13

GO Classes Set Theory And Algebra Practice Set 1 | Question: 4
Let $A$ be the set of all ordered pairs of integers, that is, $A=Z \times Z$. Define a binary relation $R$ on $A$ as follows: for all $(a, b),(c, d) \in A$ ... reflexive? Is $R$ symmetric? Is $R$ antisymmetric? Is $R$ transitive? Is $R$ an equivalence relation, a partial order, neither, or both?

Let $A$ be the set of all ordered pairs of integers, that is, $A=Z \times Z$. Define a binary relation $R$ on $A$ as follows: for all $(a, b),(c, d) \in A$,$$(a, b) R(c, ...

GO Classes

263 views

GO Classes asked May 28, 2023

4 votes

2 answers

14

GO Classes 2023 | IIITH Mock Test 1 | Question: 2
Given a set of values $\text{R} = \{1,2,3,4,5,6,7\}.$ The number of relations on this set which are both partial-order and equivalence relation is? $128$ $1$ $0$ $2^{42}$

Given a set of values $\text{R} = \{1,2,3,4,5,6,7\}.$ The number of relations on this set which are both partial-order and equivalence relation is?$128$$1$$0$$2^{42}$

GO Classes

819 views

GO Classes asked Mar 26, 2023

1 votes

2 answers

15

GO Classes Set Theory And Algebra Practice Set 1 | Question: 17
Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation? It is both symmetric and transitive It is both reflexive and transitive It is reflexive, antisymmetric, and transitive It is both reflexive and antisymmetric

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is both symmetric and transitiveIt is both reflexiv...

GO Classes

385 views

GO Classes asked May 28, 2023

1 votes

1 answer

16

GO Classes Set Theory And Algebra Practice Set 1 | Question: 16
Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation? It is both reflexive and symmetric It is only reflexive It is only antisymmetric It is both reflexive and transitive

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is both reflexive and symmetricIt is only reflexive...

GO Classes

261 views

GO Classes asked May 28, 2023

1 votes

1 answer

17

GO Classes Set Theory And Algebra Practice Set 1 | Question: 19
Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation? It is only transitive It is both antisymmetric and transitive It is both reflexive and transitive It has none of those properties

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is only transitiveIt is both antisymmetric and tran...

GO Classes

265 views

GO Classes asked May 28, 2023

1 votes

1 answer

18

GO Classes Set Theory And Algebra Practice Set 1 | Question: 18
Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation? It is only reflexive It is reflexive, symmetric, and transitive It is both reflexive and antisymmetric It is both reflexive and symmetric

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is only reflexiveIt is reflexive, symmetric, and tr...

GO Classes

354 views

GO Classes asked May 28, 2023

1 votes

1 answer

19

GO Classes Set Theory And Algebra Practice Set 1 | Question: 6
Let $A$ be any set. Subset Relation on $\mathrm{P}(\mathrm{A})$ is Anti-symmetric?

Let $A$ be any set. Subset Relation on $\mathrm{P}(\mathrm{A})$ is Anti-symmetric?

GO Classes

356 views

GO Classes asked May 28, 2023

1 votes

0 answers

20

GO Classes Set Theory And Algebra Practice Set 1 | Question: 22
Given the relation $R=\{(n, m)|n, m \in \mathbb{Z}| n,|\neq| m \mid\}$. Which of the following statements about $R$ is correct? $R$ is not an equivalence relation because it is not reflexive or ... relation because it is not antisymmetric $R$ is not an equivalence relation because it is not symmetric $R$ is an equivalence relation

Given the relation $R=\{(n, m)|n, m \in \mathbb{Z}| n,|\neq| m \mid\}$. Which of the following statements about $R$ is correct?$R$ is not an equivalence relation because ...

GO Classes

199 views

GO Classes asked May 28, 2023

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