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Recent questions tagged partial-order
27
votes
4
answers
61
GATE CSE 1998 | Question: 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 ... $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.
Kathleen
asked
in
Set Theory & Algebra
Sep 26, 2014
by
Kathleen
9.1k
views
gate1998
set-theory&algebra
normal
partial-order
descriptive
37
votes
2
answers
62
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:
Kathleen
asked
in
Set Theory & Algebra
Sep 22, 2014
by
Kathleen
10.7k
views
gatecse-2007
set-theory&algebra
normal
partial-order
descriptive
39
votes
7
answers
63
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 ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
Kathleen
asked
in
Set Theory & Algebra
Sep 19, 2014
by
Kathleen
9.9k
views
gatecse-2004
set-theory&algebra
partial-order
normal
51
votes
5
answers
64
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
Kathleen
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Kathleen
8.5k
views
gatecse-2003
set-theory&algebra
partial-order
normal
propositional-logic
16
votes
3
answers
65
GATE CSE 1991 | Question: 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.
Kathleen
asked
in
Set Theory & Algebra
Sep 12, 2014
by
Kathleen
4.2k
views
gate1991
set-theory&algebra
partial-order
normal
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