Composition of relation and transitive closure Announcing the arrival of Valued Associate...
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Composition of relation and transitive closure
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Need assistance determining whether these relations are transitive or antisymmetric (or both?)Transitive closure of these relations on ${1,2,3,4}$?Finding the smallest relation that is reflexive, transitive, and symmetricSmallest relation for reflexive, symmetry and transitivityHow to determine whether a given relation on a finite set is transitive?Symmetric closure of the reflexive closure of the transitive closure of a relationTransitive Closure, $R ={(0,0), (0,3), (1,0), (1,2), (2,0), (3,2)}$Equivalence Relation, transitive relationAm I correct about the transitive closure of this relation?binary relation that is both symmetric and irreflexive
$begingroup$
Am I right in the following?
Let $$A = {1, 2, 3, 4, 5}$$ and consider the following relation on A:
$$R = {(1, 2),(2, 3),(3, 4),(4, 5),(5, 1)}$$
a)
Here I am to find the composition of R on R. I got this:
$$R^2={(1,3),(2,4),(3,5),(4,1)}$$
b)
$$R={(1,2),(2,3),(3,4),(4,5),(5,1)}$$
The transitive closure is
$$R={(1,2),(2,3),(1,3)(3,4),(4,5),(4,1),(3,5),(5,1)}$$
EDIT1: I added (4,1), because we have (4,5),(5,1), which would be (a,b),(b,c) and the transitive closure of those would be (4,1).
discrete-mathematics
asked Mar 25 at 17:52
EventhorizonEventhorizon
153
$endgroup$
add a comment |
$begingroup$
Am I right in the following?
Let $$A = {1, 2, 3, 4, 5}$$ and consider the following relation on A:
$$R = {(1, 2),(2, 3),(3, 4),(4, 5),(5, 1)}$$
a)
Here I am to find the composition of R on R. I got this:
$$R^2={(1,3),(2,4),(3,5),(4,1)}$$
b)
$$R={(1,2),(2,3),(3,4),(4,5),(5,1)}$$
The transitive closure is
$$R={(1,2),(2,3),(1,3)(3,4),(4,5),(4,1),(3,5),(5,1)}$$
EDIT1: I added (4,1), because we have (4,5),(5,1), which would be (a,b),(b,c) and the transitive closure of those would be (4,1).
discrete-mathematics
asked Mar 25 at 17:52
EventhorizonEventhorizon
153
$endgroup$
add a comment |
$begingroup$
Am I right in the following?
Let $$A = {1, 2, 3, 4, 5}$$ and consider the following relation on A:
$$R = {(1, 2),(2, 3),(3, 4),(4, 5),(5, 1)}$$
a)
Here I am to find the composition of R on R. I got this:
$$R^2={(1,3),(2,4),(3,5),(4,1)}$$
b)
$$R={(1,2),(2,3),(3,4),(4,5),(5,1)}$$
The transitive closure is
$$R={(1,2),(2,3),(1,3)(3,4),(4,5),(4,1),(3,5),(5,1)}$$
EDIT1: I added (4,1), because we have (4,5),(5,1), which would be (a,b),(b,c) and the transitive closure of those would be (4,1).
discrete-mathematics
asked Mar 25 at 17:52
EventhorizonEventhorizon
153
$endgroup$
Am I right in the following?
Let $$A = {1, 2, 3, 4, 5}$$ and consider the following relation on A:
$$R = {(1, 2),(2, 3),(3, 4),(4, 5),(5, 1)}$$
a)
Here I am to find the composition of R on R. I got this:
$$R^2={(1,3),(2,4),(3,5),(4,1)}$$
b)
$$R={(1,2),(2,3),(3,4),(4,5),(5,1)}$$
The transitive closure is
$$R={(1,2),(2,3),(1,3)(3,4),(4,5),(4,1),(3,5),(5,1)}$$
EDIT1: I added (4,1), because we have (4,5),(5,1), which would be (a,b),(b,c) and the transitive closure of those would be (4,1).
discrete-mathematics
discrete-mathematics
asked Mar 25 at 17:52
EventhorizonEventhorizon
153
asked Mar 25 at 17:52
EventhorizonEventhorizon
153
asked Mar 25 at 17:52
EventhorizonEventhorizon
153
asked Mar 25 at 17:52
EventhorizonEventhorizon
153
asked Mar 25 at 17:52
EventhorizonEventhorizon
153
153
add a comment |
add a comment |
1 Answer
1
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$begingroup$
Not exactly.
a) You missed $(5,2)$, otherwise it's ok.
b) Try to prove that all pairs are in the transitive closure.
answered Mar 25 at 22:05
BerciBerci
62.1k23776
$endgroup$
add a comment |
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$begingroup$
Not exactly.
a) You missed $(5,2)$, otherwise it's ok.
b) Try to prove that all pairs are in the transitive closure.
answered Mar 25 at 22:05
BerciBerci
62.1k23776
$endgroup$
add a comment |
$begingroup$
Not exactly.
a) You missed $(5,2)$, otherwise it's ok.
b) Try to prove that all pairs are in the transitive closure.
answered Mar 25 at 22:05
BerciBerci
62.1k23776
$endgroup$
add a comment |
$begingroup$
Not exactly.
a) You missed $(5,2)$, otherwise it's ok.
b) Try to prove that all pairs are in the transitive closure.
answered Mar 25 at 22:05
BerciBerci
62.1k23776
$endgroup$
Not exactly.
a) You missed $(5,2)$, otherwise it's ok.
b) Try to prove that all pairs are in the transitive closure.
answered Mar 25 at 22:05
BerciBerci
62.1k23776
answered Mar 25 at 22:05
BerciBerci
62.1k23776
answered Mar 25 at 22:05
BerciBerci
62.1k23776
answered Mar 25 at 22:05
BerciBerci
62.1k23776
62.1k23776
add a comment |
add a comment |
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