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Recent questions tagged partialorder
POSET
0
votes
1
answer
1
MadeEasy Test Series: Set Thoery & Algebra  Partial Order
Let Q denote the set of rational numbers and S = {x  x belongs N ; N; x>=10} Consider the Following POSETs I. (Q ∩ [0, 1], ≤) II. (S, ≤) Which of the above POSETs are well ordered?
asked
Jan 26
in
Set Theory & Algebra
by
Badayayash
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(
1k
points)

121
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settheory&algebra
partialorder
madeeasytestseries
+1
vote
0
answers
2
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, 2018
in
Set Theory & Algebra
by
Lakshman Patel RJIT
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34.4k
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70
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discretemathematics
settheory&algebra
partialorder
0
votes
2
answers
3
Test Series
Is 1 a lattice?
asked
Sep 1, 2018
in
Set Theory & Algebra
by
Subham Nagar
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(
1.2k
points)

119
views
testseries
lattice
partialorder
discretemathematics
0
votes
2
answers
4
UGCNETJuly2018II90
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, 2018
in
Others
by
Pooja Khatri
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10.7k
points)

240
views
ugcnetjuly2018ii
discretemathematics
partialorder
+2
votes
1
answer
5
Kenneth Rosen Edition 6th Exercise 7.6 Example 21 (Page No. 519 )
How is this a lattice?
asked
Jan 25, 2018
in
Set Theory & Algebra
by
_jerry
(
353
points)

147
views
kennethrosen
discretemathematics
lattice
partialorder
+1
vote
1
answer
6
Ace Test series: Set Theory & Algebra  Partial Order
L={d,g,h,0} R={f,i,h,0} Am I doing it Correct?
asked
Jan 7, 2018
in
Set Theory & Algebra
by
Ananya Jaiswal 1
Active
(
2.2k
points)

53
views
acetestseries
settheory&algebra
partialorder
+4
votes
1
answer
7
SelfDoubt
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
(
25.3k
points)

142
views
partialorder
0
votes
0
answers
8
Kenneth Rosen Ex 7.6
asked
Nov 9, 2017
in
Set Theory & Algebra
by
Ayush Upadhyaya
Boss
(
25.3k
points)

172
views
partialorder
lattice
0
votes
0
answers
9
Self Doubt
Is the dual of TOSET, a TOSET always?
asked
Nov 9, 2017
in
Set Theory & Algebra
by
Ayush Upadhyaya
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(
25.3k
points)

67
views
partialorder
+1
vote
2
answers
10
Set Relation
Answer please explain the ans. R is antisymmetric then aRb, bRa > a=b so ab=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)

228
views
engineeringmathematics
settheory&algebra
equivalencerelation
partialorder
antisymmetric
+2
votes
1
answer
11
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
(
367
points)

295
views
engineeringmathematics
relations
relationalalgebra
partialorder
settheory&algebra
0
votes
2
answers
12
UGCNETDec2010II3
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
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(
41.1k
points)

347
views
ugcnetdec2010ii
discretemathematics
partialorder
+5
votes
1
answer
13
Discrete MAthematics question **** imp
asked
Jul 4, 2016
in
Set Theory & Algebra
by
LavTheRawkstar
Active
(
5.2k
points)

1.4k
views
lattice
partialorder
0
votes
4
answers
14
Ace Test Series: Set Theory & Algebra  Partial Order
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)

186
views
acetestseries
engineeringmathematics
discretemathematics
settheory&algebra
partialorder
+9
votes
3
answers
15
TIFR2014B16
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
(
41.1k
points)

830
views
tifr2014
settheory&algebra
partialorder
+9
votes
2
answers
16
TIFR2014B15
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 nonempty subset of ... Every nonempty subset of $N^{*}$ has a greatest lower bound. Every nonempty finite subset of $N^{*}$ has a least upper bound.
asked
Nov 20, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
41.1k
points)

619
views
tifr2014
settheory&algebra
partialorder
+5
votes
3
answers
17
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
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(
30.9k
points)

880
views
partialorder
booleanalgebra
lattice
engineeringmathematics
settheory&algebra
+2
votes
2
answers
18
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
(
40.9k
points)

580
views
partialorder
+10
votes
4
answers
19
TIFR2013B4
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
(
41.1k
points)

584
views
tifr2013
settheory&algebra
partialorder
+8
votes
2
answers
20
TIFR2012B5
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
(
41.1k
points)

434
views
tifr2012
settheory&algebra
partialorder
+16
votes
5
answers
21
GATE2007IT23
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)

2.1k
views
gate2007it
settheory&algebra
partialorder
normal
+13
votes
3
answers
22
GATE19961.2
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
(
59.8k
points)

1.1k
views
gate1996
settheory&algebra
partialorder
normal
+11
votes
3
answers
23
GATE19938.5
The lessthan 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
(
59.8k
points)

1.1k
views
gate1993
settheory&algebra
partialorder
easy
+22
votes
1
answer
24
GATE19976.1
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
(
59.8k
points)

2k
views
gate1997
settheory&algebra
partialorder
normal
+16
votes
2
answers
25
GATE199811
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
(
59.8k
points)

1.3k
views
gate1998
settheory&algebra
normal
partialorder
descriptive
+22
votes
2
answers
26
GATE200726
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
(
59.8k
points)

3.2k
views
gate2007
settheory&algebra
normal
partialorder
descriptive
+24
votes
7
answers
27
GATE200473
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
(
59.8k
points)

2.4k
views
gate2004
settheory&algebra
partialorder
normal
+29
votes
2
answers
28
GATE200331
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
(
59.8k
points)

2.5k
views
gate2003
settheory&algebra
partialorder
normal
propositionallogic
+11
votes
2
answers
29
GATE199101,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
(
59.8k
points)

1.1k
views
gate1991
settheory&algebra
partialorder
normal
descriptive
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