Question

Given a preorder R on a set A, prove that there is an equivalence relation S...

Given a preorder R on a set A, prove that there is an equivalence relation S on A and a partial ordering ≤ on A/S such that [a] S ≤ [b] S ⇐⇒ aRb.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
a) Let R be an equivalence relation defined on some set A. Prove using induction that...
a) Let R be an equivalence relation defined on some set A. Prove using induction that R^n is also an equivalence relation. Note: In order to prove transitivity, you may use the fact that R is transitive if and only if R^n⊆R for ever positive integer ​n b) Prove or disprove that a partial order cannot have a cycle.
A relation R on a set A is called circular if for all a,b,c in A,...
A relation R on a set A is called circular if for all a,b,c in A, aRb and bRc imply cRa. Prove that a relation is an equivalence relation iff it is reflexive and circular.
Prove that the relation of set equivalence is an equivalence relation.
Prove that the relation of set equivalence is an equivalence relation.
Let ​R​ be an equivalence relation defined on some set ​A​. Prove using mathematical induction that...
Let ​R​ be an equivalence relation defined on some set ​A​. Prove using mathematical induction that ​R​^n​ is also an equivalence relation.
Let R be the relation on Z defined by: For any a, b ∈ Z ,...
Let R be the relation on Z defined by: For any a, b ∈ Z , aRb if and only if 4 | (a + 3b). (a) Prove that R is an equivalence relation. (b) Prove that for all integers a and b, aRb if and only if a ≡ b (mod 4)
For each of the following, prove that the relation is an equivalence relation. Then give the...
For each of the following, prove that the relation is an equivalence relation. Then give the information about the equivalence classes, as specified. a) The relation ∼ on R defined by x ∼ y iff x = y or xy = 2. Explicitly find the equivalence classes [2], [3], [−4/5 ], and [0] b) The relation ∼ on R+ × R+ defined by (x, y) ∼ (u, v) iff x2v = u2y. Explicitly find the equivalence classes [(5, 2)] and...
Let A be a non-empty set. Prove that if ∼ defines an equivalence relation on the...
Let A be a non-empty set. Prove that if ∼ defines an equivalence relation on the set A, then the set of equivalence classes of ∼ form a partition of A.
Define a relation R on Z by aRb if and only if |a| = |b|. a)...
Define a relation R on Z by aRb if and only if |a| = |b|. a) Prove R is an equivalence relation b) Compute [0] and [n] for n in Z with n different than 0.
Prove that the relation R on the set of all people, defined by xRy if x...
Prove that the relation R on the set of all people, defined by xRy if x and y have the same first name is an equivalence relation.
There is no equivalence relation R on set {a, b, c, d, e} such that R...
There is no equivalence relation R on set {a, b, c, d, e} such that R contains less than 5 ordered pairs (True or False)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT