Question

4. Let A={(1,3),(2,4),(-4,-8),(3,9),(1,5),(3,6)}. The relation R is defined on A as follows: For all (a, b),(c,...

4. Let A={(1,3),(2,4),(-4,-8),(3,9),(1,5),(3,6)}. The relation R is defined on A as follows: For all (a, b),(c, d) ∈ A, (a, b) R (c, d) ⇔ ad = bc . R is an equivalence relation. Find the distinct equivalence classes of R.

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 = {1,2,3,4,5,6,7,8,9,10} define the equivalence relation R on A as follows : For all...
Let A = {1,2,3,4,5,6,7,8,9,10} define the equivalence relation R on A as follows : For all x,y A, xRy <=> 3|(x-y) . Find the distinct equivalence classes of R(discrete math)
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...
13. Let R be a relation on Z × Z be defined as (a, b) R...
13. Let R be a relation on Z × Z be defined as (a, b) R (c, d) if and only if a + d = b + c. a. Prove that R is an equivalence relation on Z × Z. b. Determine [(2, 3)].
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)
Define a relation on N x N by (a, b)R(c, d) iff ad=bc a. Show that...
Define a relation on N x N by (a, b)R(c, d) iff ad=bc a. Show that R is an equivalence relation. b. Find the equivalence class E(1, 2)
Let N* be the set of positive integers. The relation ∼ on N* is defined as...
Let N* be the set of positive integers. The relation ∼ on N* is defined as follows: m ∼ n ⇐⇒ ∃k ∈ N* mn = k2 (a) Prove that ∼ is an equivalence relation. (b) Find the equivalence classes of 2, 4, and 6.
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x,...
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x, y) ∈ R if and only if x + 2 > y. For example, (4, 3) is in R because 4 + 2 = 6, which is greater than 3. (a) Is the relation reflexive? Prove or disprove. (b) Is the relation symmetric? Prove or disprove. (c) Is the relation transitive? Prove or disprove. (d) Is it an equivalence relation? Explain.
Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation...
Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation R on A as follows: For all (m, n) is in A, m R n ⇔ 5|(m2 − n2). It is a fact that R is an equivalence relation on A. Use set-roster notation to list the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.) ____________
Recall from class that we defined the set of integers by defining the equivalence relation ∼...
Recall from class that we defined the set of integers by defining the equivalence relation ∼ on N × N by (a, b) ∼ (c, d) =⇒ a + d = c + b, and then took the integers to be equivalence classes for this relation, i.e. Z = [(a, b)]∼ | (a, b) ∈ N × N . We then proceeded to define 0Z = [(0, 0)]∼, 1Z = [(1, 0)]∼, − [(a, b)]∼ = [(b, a)]∼, [(a, b)]∼...
Let p and q be any two distinct prime numbers and define the relation a R...
Let p and q be any two distinct prime numbers and define the relation a R b on integers a,b by: a R b iff b-a is divisible by both p and q. For this relation R: Show that the equivalence classes of R correspond to the elements of  ℤpq. That is: [a] = [b] as equivalence classes of R if and only if [a] = [b] as elements of ℤpq. you may use the following lemma: If p is prime...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT