How many equivalence classes does this equivalence relation have?Equivalence classes for a Relation on a product set.Help with partitions, equivalence classes, equivalence relations.Equivalence relation and equivalence classes given function and relationEquivalence classes with this relation equivalenceDoes the relation $R = (x,y) in ℝ^+ times ℝ^+ $ create a partition for a set $A = 1,2,3,4,5,6,7,8,9,10$? If so, why?On the equivalence classes of a relation (Myhill-Nerode theorem)Breaking an equivalence relation into equivalence classesClasses of an equivalence relationFinding the equivalence classes of a singleton setCounting the number of equivalence classes (expecting 7 from the DFA states but seeing only 6)
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How many equivalence classes does this equivalence relation have?
Equivalence classes for a Relation on a product set.Help with partitions, equivalence classes, equivalence relations.Equivalence relation and equivalence classes given function and relationEquivalence classes with this relation equivalenceDoes the relation $R = ( x $ create a partition for a set $A = 1,2,3,4,5,6,7,8,9,10$? If so, why?On the equivalence classes of a relation (Myhill-Nerode theorem)Breaking an equivalence relation into equivalence classesClasses of an equivalence relationFinding the equivalence classes of a singleton setCounting the number of equivalence classes (expecting 7 from the DFA states but seeing only 6)
$begingroup$
Let Σ=0,1, ≡L is an equivalence relation for set L Let s = 10100 and L = s be the language containing only string s
L−x = y:xy∈L
x ≡L y ⟺ L−x = L−y
I can count 6:
L-empty
L-1
L-10
L-101
L-1010
L-10100
However I believe the there should be 7 states here. Can anyone point out what I'm missing please?
What would "the partition of Σ∗ in the equivalence classes of ≡L." be then?
Thanks for any help!
relations equivalence-relations
asked Mar 11 at 10:38
Jay.FJay.F
82
New contributor
Jay.F is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Let Σ=0,1, ≡L is an equivalence relation for set L Let s = 10100 and L = s be the language containing only string s
L−x = y:xy∈L
x ≡L y ⟺ L−x = L−y
I can count 6:
L-empty
L-1
L-10
L-101
L-1010
L-10100
However I believe the there should be 7 states here. Can anyone point out what I'm missing please?
What would "the partition of Σ∗ in the equivalence classes of ≡L." be then?
Thanks for any help!
relations equivalence-relations
asked Mar 11 at 10:38
Jay.FJay.F
82
New contributor
Jay.F is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
What about all the other strings such as $0$, $00$, $01$, $11$ etc. for which $L-x=$ ?
$endgroup$
– gandalf61
Mar 11 at 15:46
$begingroup$
An equivalence relation for a set L can only partition L and no others sets. As L is a singleton set, there is exactly one equivalence class, namely L.
$endgroup$
– William Elliot
Mar 12 at 2:47
add a comment |
$begingroup$
Let Σ=0,1, ≡L is an equivalence relation for set L Let s = 10100 and L = s be the language containing only string s
L−x = y:xy∈L
x ≡L y ⟺ L−x = L−y
I can count 6:
L-empty
L-1
L-10
L-101
L-1010
L-10100
However I believe the there should be 7 states here. Can anyone point out what I'm missing please?
What would "the partition of Σ∗ in the equivalence classes of ≡L." be then?
Thanks for any help!
relations equivalence-relations
asked Mar 11 at 10:38
Jay.FJay.F
82
New contributor
Jay.F is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Let Σ=0,1, ≡L is an equivalence relation for set L Let s = 10100 and L = s be the language containing only string s
L−x = y:xy∈L
x ≡L y ⟺ L−x = L−y
I can count 6:
L-empty
L-1
L-10
L-101
L-1010
L-10100
However I believe the there should be 7 states here. Can anyone point out what I'm missing please?
What would "the partition of Σ∗ in the equivalence classes of ≡L." be then?
Thanks for any help!
relations equivalence-relations
relations equivalence-relations
asked Mar 11 at 10:38
Jay.FJay.F
82
New contributor
Jay.F is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 11 at 10:38
Jay.FJay.F
82
New contributor
Jay.F is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 11 at 10:38
Jay.FJay.F
82
New contributor
Jay.F is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 11 at 10:38
Jay.FJay.F
82
asked Mar 11 at 10:38
Jay.FJay.F
82
82
New contributor
Jay.F is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Jay.F is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Jay.F is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
What about all the other strings such as $0$, $00$, $01$, $11$ etc. for which $L-x=$ ?
$endgroup$
– gandalf61
Mar 11 at 15:46
$begingroup$
An equivalence relation for a set L can only partition L and no others sets. As L is a singleton set, there is exactly one equivalence class, namely L.
$endgroup$
– William Elliot
Mar 12 at 2:47
add a comment |
$begingroup$
What about all the other strings such as $0$, $00$, $01$, $11$ etc. for which $L-x=$ ?
$endgroup$
– gandalf61
Mar 11 at 15:46
$begingroup$
An equivalence relation for a set L can only partition L and no others sets. As L is a singleton set, there is exactly one equivalence class, namely L.
$endgroup$
– William Elliot
Mar 12 at 2:47
$begingroup$
What about all the other strings such as $0$, $00$, $01$, $11$ etc. for which $L-x=$ ?
$endgroup$
– gandalf61
Mar 11 at 15:46
$begingroup$
What about all the other strings such as $0$, $00$, $01$, $11$ etc. for which $L-x=$ ?
$endgroup$
– gandalf61
Mar 11 at 15:46
$begingroup$
An equivalence relation for a set L can only partition L and no others sets. As L is a singleton set, there is exactly one equivalence class, namely L.
$endgroup$
– William Elliot
Mar 12 at 2:47
$begingroup$
An equivalence relation for a set L can only partition L and no others sets. As L is a singleton set, there is exactly one equivalence class, namely L.
$endgroup$
– William Elliot
Mar 12 at 2:47
add a comment |
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$begingroup$
What about all the other strings such as $0$, $00$, $01$, $11$ etc. for which $L-x=$ ?
$endgroup$
– gandalf61
Mar 11 at 15:46
$begingroup$
An equivalence relation for a set L can only partition L and no others sets. As L is a singleton set, there is exactly one equivalence class, namely L.
$endgroup$
– William Elliot
Mar 12 at 2:47