Recent questions tagged partial-order

+1 vote

0 answers

1

Partial and Total Order
The set of all English words ordered in a dictionary is ________ $A)$ not a poset $B)$ a poset but not totally ordered $C)$ a totally ordered set but not well ordered $D)$ a well ordered set

asked Oct 6 in Set Theory & Algebra by Lakshman Patel RJIT Boss (20.8k points) | 25 views

0 votes

2 answers

2

Test Series
Is 1 a lattice?

asked Sep 1 in Set Theory & Algebra by Subham Nagar Junior (889 points) | 73 views

0 votes

3 answers

3

UGCNET-July-2018-II-90
Which of the following statements is true? $(Z, \leq)$ is not totally ordered The set inclusion relation $\subseteq$ is a partial ordering on the power set of a set S $(Z, \neq)$ is a poset The directed graph is not a partial order

asked Jul 13 in Others by Pooja Khatri Active (5.1k points) | 135 views

+4 votes

1 answer

4

Self-Doubt
Is the Poset (Q,Less than or equal to) a well ordered set? Where Q denotes set of all rational numbers and relation R is less than or equal to.

asked Nov 9, 2017 in Set Theory & Algebra by Ayush Upadhyaya Boss (19k points) | 116 views

0 votes

0 answers

5

Kenneth Rosen Ex 7.6

asked Nov 9, 2017 in Set Theory & Algebra by Ayush Upadhyaya Boss (19k points) | 148 views

0 votes

0 answers

6

Self Doubt
Is the dual of TOSET, a TOSET always?

asked Nov 9, 2017 in Set Theory & Algebra by Ayush Upadhyaya Boss (19k points) | 59 views

+1 vote

2 answers

7

Set Relation
Answer please explain the ans. R is antisymmetric then aRb, bRa -> a=b so a-b=0 and 0 is not odd positive then how it is antisymmetric?

asked Aug 11, 2017 in Set Theory & Algebra by Dilip Puri (235 points) | 181 views

+1 vote

1 answer

8

Relation and Partial order
Is (S, R) a poset if S is the set of all people in the world and (a, b) ∈ R, where a and b are people, if a is not taller than b?

asked Jul 7, 2017 in Set Theory & Algebra by ram_18051996 (375 points) | 270 views

0 votes

2 answers

9

UGCNET-Dec2010-II-3
A partially ordered set is said to be a lattice if every two elements in the set have A unique least upper bound A unique greatest lower bound Both $(A)$ and $(B)$ None of the above

asked Sep 5, 2016 in Discrete Mathematics by makhdoom ghaya Boss (40.5k points) | 297 views

+5 votes

1 answer

10

Discrete MAthematics question **** imp

asked Jul 4, 2016 in Set Theory & Algebra by LavTheRawkstar Active (5.2k points) | 1.3k views

0 votes

4 answers

11

Which relations are partial orders?
Argument: R2 is straight away eliminated. For R3, to satisfy Antisymmetric relation.. Say -2 and +2 satisfy it then +2 and -2 should not satisfy. But its not the case. Answer is given as C. Am I so blind that I couldn't figure out my mistake?

asked Jan 30, 2016 in Set Theory & Algebra by Tushar Shinde Active (2.7k points) | 171 views

+9 votes

3 answers

12

TIFR2014-B-16
Consider the ordering relation $x\mid y \subseteq N \times N$ over natural numbers $N$ such that $x \mid y$ if there exists $z \in N$ such that $x ∙ z = y$. A set is called lattice if every finite subset has a least upper bound and greatest lower bound. It ... $\mid$ is a total order. $(N, \mid)$ is a complete lattice. $(N, \mid)$ is a lattice but not a complete lattice.

asked Nov 20, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (40.5k points) | 769 views

+9 votes

2 answers

13

TIFR2014-B-15
Consider the set $N^{*}$ of finite sequences of natural numbers with $x \leq_{p}y$ denoting that sequence $x$ is a prefix of sequence $y$. Then, which of the following is true? $N^{*}$ is uncountable. $\leq_{p}$ is a total order. Every non-empty subset of ... Every non-empty subset of $N^{*}$ has a greatest lower bound. Every non-empty finite subset of $N^{*}$ has a least upper bound.

asked Nov 20, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (40.5k points) | 569 views

+5 votes

3 answers

14

Boolean Algebra
Consider a Hasse Diagram for a Boolean Algebra of Order 3 What can we comment about it? How is it successfully able to represent the Boolean Algebra System? Is there an easy way to check for distributive lattice, or any other properties of a lattice? ... that one should provide a complete answer to all parts of the question. Whatever one can supply to support its answer is welcomed.

asked Nov 11, 2015 in Set Theory & Algebra by amarVashishth Boss (30.9k points) | 810 views

+2 votes

2 answers

15

Number of edges in the Hasse Diagram of a boolean algebra with 8 elements.

asked Nov 11, 2015 in Set Theory & Algebra by LeenSharma Boss (40.7k points) | 528 views

+10 votes

4 answers

16

TIFR2013-B-4
A set $S$ together with partial order $\ll$ is called a well order if it has no infinite descending chains, i.e. there is no infinite sequence $x_1, x_2,\ldots$ of elements from $S$ such that $x_{i+1} \ll x_i$ and $x_{i+1} \neq x_i$ for all $i$. Consider the set of ... are only $2^{24}$ words. $W$ is not a partial order. $W$ is a partial order but not a well order. $W$ is a well order.

asked Nov 6, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (40.5k points) | 548 views

+7 votes

2 answers

17

TIFR2012-B-5
Let $R$ be a binary relation over a set $S$. The binary relation $R$ ... $\sqsubseteq $ is an equivalence relation and a well order. $\sqsubseteq $ is neither a partial order nor an equivalence relation.

asked Oct 31, 2015 in Set Theory & Algebra by makhdoom ghaya Boss (40.5k points) | 395 views

+14 votes

5 answers

18

GATE2007-IT-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 $(\frac{a}{10},\frac{b}{10})\in P.$ Consider the ... $P$? (i) and (iii) (ii) and (iv) (i) and (iv) (iii) and (iv)

asked Oct 30, 2014 in Set Theory & Algebra by Ishrat Jahan Boss (19.1k points) | 1.8k views

+13 votes

3 answers

19

GATE1996-1.2
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

asked Oct 9, 2014 in Set Theory & Algebra by Kathleen Veteran (59.7k points) | 981 views

+11 votes

3 answers

20

GATE1993-8.5
The less-than relation, $<,$ on reals is a partial ordering since it is asymmetric and reflexive a partial ordering since it is antisymmetric and reflexive not a partial ordering because it is not asymmetric and not reflexive not a partial ordering because it is not antisymmetric and reflexive none of the above

asked Sep 30, 2014 in Set Theory & Algebra by Kathleen Veteran (59.7k points) | 961 views

+21 votes

1 answer

21

GATE1997-6.1
A partial order ≤ is defined on the set $S$ $=$ $\left \{ x, a1, a2, ... an, y \right \}$ as $x$ $\leq _{i}$ $a_{i}$ for all $i$ and $a_{i}\leq y$ for all $i$, where $n ≥ 1$. The number of total orders on the set S which contain the partial order $≤$ is $n!$ $n+2$ $n$ $1$

asked Sep 29, 2014 in Set Theory & Algebra by Kathleen Veteran (59.7k points) | 1.8k views

+15 votes

2 answers

22

GATE1998-11
Suppose $A = \{a, b, c, d\}$ and $\Pi_1$ is the following partition of A $\Pi_1 = \left\{\left\{a, b, c\right\}\left\{d\right\}\right\}$ List the ordered pairs of the equivalence relations induced by $\Pi_1$. Draw the graph of the above equivalence relation ... $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.

asked Sep 26, 2014 in Engineering Mathematics by Kathleen Veteran (59.7k points) | 1.1k views

+20 votes

2 answers

23

GATE2007-26
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:

asked Sep 22, 2014 in Set Theory & Algebra by Kathleen Veteran (59.7k points) | 2.7k views

+22 votes

7 answers

24

GATE2004-73
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 set containment ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$

asked Sep 19, 2014 in Set Theory & Algebra by Kathleen Veteran (59.7k points) | 2k views

+28 votes

2 answers

25

GATE2003-31
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 $x \leq y$ ... False 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

asked Sep 16, 2014 in Set Theory & Algebra by Kathleen Veteran (59.7k points) | 2.1k views

+10 votes

2 answers

26

GATE1991-01,xiv
If the longest chain in a partial order is of length $n$, then the partial order can be written as a _____ of $n$ antichains.

asked Sep 12, 2014 in Set Theory & Algebra by Kathleen Veteran (59.7k points) | 899 views

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