Question

Define a relation ? over the set of nonzero rational numbers as ??? if and only...

Define a relation ? over the set of nonzero rational numbers as ??? if and only if ??>0. Is R 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
For natural numbers x and y, define xRy if and only if x^2 + y is...
For natural numbers x and y, define xRy if and only if x^2 + y is even. Prove that R is an equivalence relation on the set of natural numbers and find the quotient set determined by R. What would the quotient set be? can this proof be explained in detail?
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.
Let R be a relation on set RxR of ordered pairs of real numbers such that...
Let R be a relation on set RxR of ordered pairs of real numbers such that (a,b)R(c,d) if a+d=b+c. Prove that R is an equivalence relation and find equivalence class [(0,b)]R
Suppose we define the relation R on the set of all people by the rule "a...
Suppose we define the relation R on the set of all people by the rule "a R b if and only if a is Facebook friends with b." Is this relation reflexive?  Is is symmetric?   Is it transitive?   Is it an equivalence relation? Briefly but clearly justify your answers.
Let S be the collection of all sequences of real numbers and define a relation on...
Let S be the collection of all sequences of real numbers and define a relation on S by {xn} ∼ {yn} if and only if {xn − yn} converges to 0. a) Prove that ∼ is an equivalence relation on S. b) What happens if ∼ is defined by {xn} ∼ {yn} if and only if {xn + yn} converges to 0?
Let R be the relation on the set of real numbers such that xRy if and...
Let R be the relation on the set of real numbers such that xRy if and only if x and y are real numbers that differ by less than 1, that is, |x − y| < 1. Which of the following pair or pairs can be used as a counterexample to show this relation is not an equivalence relation? A) (1, 1) B) (1, 1.8), (1.8, 3) C) (1, 1), (3, 3) D) (1, 1), (1, 1.5)
Let R = {(x, y) | x − y is an integer} be a relation on...
Let R = {(x, y) | x − y is an integer} be a relation on the set Q of rational numbers. a) [6 marks] Prove that R is an equivalence relation on Q. b) [2 marks] What is the equivalence class of 0? c) [2 marks] What is the equivalence class of 1/2?
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...
1. We define a relation C on the set of humans as xRy ⇐⇒ x and...
1. We define a relation C on the set of humans as xRy ⇐⇒ x and y were born in the same country Describe the equivalence class containing yourself as an element. 2. Let R be an equivalence relation with (x, y) ∈ R and (y, z) is not ∈ R (that is, y does not relate to z). Can you determine whether or not xRz? Why or why not?
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. I need to prove that: a) R is an equivalence relation. (which I have) b) 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 I...