prove that for the equivalence class : X/(X/E) = E
Let E be an equivalence relation on the set X .
prove that: X / (X / E) = E
The definition of euivalence class: x/E = { for every y in the X | xEy }
The set of all equivalence classes: X/E = { x/E | x is a member of X }
relations equivalence-relations
asked Nov 22 '18 at 22:13
YahyaYahya
106
add a comment |
Let E be an equivalence relation on the set X .
prove that: X / (X / E) = E
The definition of euivalence class: x/E = { for every y in the X | xEy }
The set of all equivalence classes: X/E = { x/E | x is a member of X }
relations equivalence-relations
asked Nov 22 '18 at 22:13
YahyaYahya
106
1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 '18 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 '18 at 8:03
1
Ok. So how is X/E, a collection of subsets of X, an equivalence relation. X/E subset P(X). Equivalence relations for X are subsets of X×X.
– William Elliot
Nov 23 '18 at 11:39
add a comment |
Let E be an equivalence relation on the set X .
prove that: X / (X / E) = E
The definition of euivalence class: x/E = { for every y in the X | xEy }
The set of all equivalence classes: X/E = { x/E | x is a member of X }
relations equivalence-relations
asked Nov 22 '18 at 22:13
YahyaYahya
106
Let E be an equivalence relation on the set X .
prove that: X / (X / E) = E
The definition of euivalence class: x/E = { for every y in the X | xEy }
The set of all equivalence classes: X/E = { x/E | x is a member of X }
relations equivalence-relations
relations equivalence-relations
asked Nov 22 '18 at 22:13
YahyaYahya
106
asked Nov 22 '18 at 22:13
YahyaYahya
106
edited Nov 23 '18 at 8:01
Yahya
asked Nov 22 '18 at 22:13
YahyaYahya
106
asked Nov 22 '18 at 22:13
YahyaYahya
106
asked Nov 22 '18 at 22:13
YahyaYahya
106
106
1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 '18 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 '18 at 8:03
1
Ok. So how is X/E, a collection of subsets of X, an equivalence relation. X/E subset P(X). Equivalence relations for X are subsets of X×X.
– William Elliot
Nov 23 '18 at 11:39
add a comment |
1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 '18 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 '18 at 8:03
1
Ok. So how is X/E, a collection of subsets of X, an equivalence relation. X/E subset P(X). Equivalence relations for X are subsets of X×X.
– William Elliot
Nov 23 '18 at 11:39
1
1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 '18 at 2:07
You defined x/E but did not define X/E.
– William Elliot
Nov 23 '18 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 '18 at 8:03
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 '18 at 8:03
1
1
Ok. So how is X/E, a collection of subsets of X, an equivalence relation. X/E subset P(X). Equivalence relations for X are subsets of X×X.
– William Elliot
Nov 23 '18 at 11:39
Ok. So how is X/E, a collection of subsets of X, an equivalence relation. X/E subset P(X). Equivalence relations for X are subsets of X×X.
– William Elliot
Nov 23 '18 at 11:39
add a comment |
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1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 '18 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 '18 at 8:03
1
Ok. So how is X/E, a collection of subsets of X, an equivalence relation. X/E subset P(X). Equivalence relations for X are subsets of X×X.
– William Elliot
Nov 23 '18 at 11:39