prove that for the equivalence class : X/(X/E) = E
up vote
0
down vote
favorite
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 at 22:13
Yahya
175
add a comment |
up vote
0
down vote
favorite
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 at 22:13
Yahya
175
1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 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 at 11:39
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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 at 22:13
Yahya
175
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 at 22:13
Yahya
175
asked Nov 22 at 22:13
Yahya
175
edited Nov 23 at 8:01
asked Nov 22 at 22:13
Yahya
175
asked Nov 22 at 22:13
Yahya
175
asked Nov 22 at 22:13
Yahya
175
175
1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 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 at 11:39
add a comment |
1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 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 at 11:39
1
1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 at 2:07
You defined x/E but did not define X/E.
– William Elliot
Nov 23 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 at 8:03
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 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 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 at 11:39
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3009735%2fprove-that-for-the-equivalence-class-x-x-e-e%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
You defined x/E but did not define X/E.
– William Elliot
Nov 23 at 2:07
@WilliamElliot Yes you are right. I have edited the information and appended the definition of X/E.
– Yahya
Nov 23 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 at 11:39