Recent questions tagged partial-order

+4 votes

1 answer

1

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 (11k points) | 91 views

0 votes

0 answers

2

Kenneth Rosen Ex 7.6

asked Nov 9, 2017 in Set Theory & Algebra by Ayush Upadhyaya Boss (11k points) | 116 views

0 votes

0 answers

3

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

asked Nov 9, 2017 in Set Theory & Algebra by Ayush Upadhyaya Boss (11k points) | 55 views

+1 vote

2 answers

4

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) | 138 views

+1 vote

1 answer

5

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 (355 points) | 243 views

+5 votes

1 answer

6

Discrete MAthematics question **** imp

asked Jul 4, 2016 in Set Theory & Algebra by LavTheRawkstar Active (5.1k points) | 1.2k views

0 votes

4 answers

7

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 (2.6k points) | 165 views

+7 votes

3 answers

8

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 is ... $\mid$ 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 (40.1k points) | 649 views

+8 votes

1 answer

9

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 $N ... 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 (40.1k points) | 486 views

+5 votes

3 answers

10

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 (30.7k points) | 760 views

+2 votes

2 answers

11

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 (40.3k points) | 495 views

+9 votes

4 answers

12

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 ... 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 (40.1k points) | 476 views

+5 votes

2 answers

13

TIFR2012-B-5
Let $R$ be a binary relation over a set $S$. The binary relation $R$ is called an equivalence relation if it is reflexive transitive and symmetric. The relation is called partial order if it is reflexive, transitive and anti symmetric. (Notation: Let ... 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 (40.1k points) | 340 views

+14 votes

5 answers

14

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 ... , 153)$ Which of these ordered pairs of natural numbers are contained in $P$? (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) | 1.5k views

+10 votes

3 answers

15

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 (59.5k points) | 841 views

+10 votes

3 answers

16

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 (59.5k points) | 812 views

+20 votes

1 answer

17

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 (59.5k points) | 1.5k views

+13 votes

2 answers

18

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. ... }$ Draw a Poset diagram of the poset, $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.

asked Sep 26, 2014 in Engineering Mathematics by Kathleen Veteran (59.5k points) | 874 views

+16 votes

2 answers

19

GATE2007-26
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ $\quad π_3 = \{\overline{abc}, \overline{d}\},\quad π_4 =\{\bar{a}, \ ... $S' = \{π_1,π_2,π_3,π_4\}$ defined as follows: $π_i \prec π_j$ 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 (59.5k points) | 2.3k views

+20 votes

7 answers

20

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? ... \{2, 3\}$ $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$

asked Sep 19, 2014 in Set Theory & Algebra by Kathleen Veteran (59.5k points) | 1.7k views

+26 votes

2 answers

21

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 $x \leq y$, where $\ ... 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 (59.5k points) | 1.8k views

+8 votes

2 answers

22

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 (59.5k points) | 739 views

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