Question

"Prove that, for the equivalence classes [a,b] and operations + and x: the distributive law for...

"Prove that, for the equivalence classes [a,b] and operations + and x: the distributive law for x over + is true"

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
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...
Determine the distance equivalence classes for the relation R is defined on ℤ by a R...
Determine the distance equivalence classes for the relation R is defined on ℤ by a R b if |a - 2| = |b - 2|. I had to prove it was an equivalence relation as well, but that part was not hard. Just want to know if the logic and presentation is sound for the last part: 8.48) A relation R is defined on ℤ by a R b if |a - 2| = |b - 2|. Prove that R...
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.
Abstract Algebra I Corollary 1.26- Two equivalence classes of an equivalence relation are either disjoint or...
Abstract Algebra I Corollary 1.26- Two equivalence classes of an equivalence relation are either disjoint or equal. Corollary 2.11- Let a and b be two integers that are relatively prime. Then there exist integers r and s such that ar+bs=1. PLEASE ANSWER THE FOLLOWING: 1) Why is Corollary 1.26 true? 2) Why is Corollary 2.11 true?
9e) fix n ∈ ℕ. Prove congruence modulo n is an equivalence relation on ℤ. How...
9e) fix n ∈ ℕ. Prove congruence modulo n is an equivalence relation on ℤ. How many equivalence classes does it have? 9f) fix n ∈ ℕ. Prove that if a ≡ b mod n and c ≡ d mod n then a + c ≡b + d mod n. 9g) fix n ∈ ℕ.Prove that if a ≡ b mod n and c ≡ d mod n then ac ≡bd mod n.
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.
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.
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.
Let H be a subgroup of a group G. Let ∼H and ρH be the equivalence...
Let H be a subgroup of a group G. Let ∼H and ρH be the equivalence relation in G introduced in class given by x∼H y⇐⇒x−1y∈H, xρHy⇐⇒xy−1 ∈H. The equivalence classes are the left and the right cosets of H in G, respectively. Prove that the functionφ: G/∼H →G/ρH given by φ(xH) = Hx−1 is well-defined and bijective. This proves that the number of left and right cosets are equal.
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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT