Question

Prove that the relation of set equivalence is an equivalence relation.

Prove that the relation of set equivalence is an equivalence relation.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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.
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.
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.
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.
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...
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.
Suppose R is an equivalence relation on a finite set A, and every equivalence class has...
Suppose R is an equivalence relation on a finite set A, and every equivalence class has the same cardinality m. Express |R| in terms of m and |A|. Explain why the answer is m|A|
On set R2 define ∼ by writing(a,b)∼(u,v)⇔ 2a−b = 2u−v. Prove that∼is an equivalence relation on...
On set R2 define ∼ by writing(a,b)∼(u,v)⇔ 2a−b = 2u−v. Prove that∼is an equivalence relation on R2 In the previous problem: (1) Describe [(1,1)]∼. (That is formulate a statement P(x,y) such that [(1,1)]∼ = {(x,y) ∈ R2 | P(x,y)}.) (2) Describe [(a, b)]∼ for any given point (a, b). (3) Plot sets [(1,1)]∼ and [(0,0)]∼ in R2.
Let ~ be an equivalence relation on a given set A. Show [a] = [b] if...
Let ~ be an equivalence relation on a given set A. Show [a] = [b] if and only if a ~ b, for all a,b exists in A.
Consider the following relation ∼ on the set of integers a ∼ b ⇐⇒ b 2...
Consider the following relation ∼ on the set of integers a ∼ b ⇐⇒ b 2 − a 2 is divisible by 3 Prove that this is an equivalence relation. List all equivalence classes.