Question

A relation R is defined on Z by aRb if |a−b| ≤ 2. Which of the...

A relation R is defined on Z by aRb if |a−b| ≤ 2. Which of the properties reflexive, symmetric and transitive does the relation R possess? Explain why If R does not possess one of these properties,

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
the relation R on the set of all people where aRb means that a is younger...
the relation R on the set of all people where aRb means that a is younger than b. Determine if R is: reflexive symmetric transitive antisymmetric
2. Let R be a relation on the set of integers ℤ defined by ? =...
2. Let R be a relation on the set of integers ℤ defined by ? = {(?, ?): a2 + ?2 ?? ? ??????? ??????} Is this relation reflexive? Symmetric? transitive?
A relation R is defined on Z by aRb if 7x − 5y is even. Show...
A relation R is defined on Z by aRb if 7x − 5y is even. Show that R is an equivalence relation.
Consider the relation R defined on the real line R, and defined as follows: x ∼...
Consider the relation R defined on the real line R, and defined as follows: x ∼ y if and only if the distance from the point x to the point y is less than 3. Study if this relation is reflexive, symmetric, and transitive. Which points are related to 2?
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 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)
Determine whether the binary relation R on {a, b, c}   where R={(a, a), (b, b)), (c,...
Determine whether the binary relation R on {a, b, c}   where R={(a, a), (b, b)), (c, c), (a, b), (a, c), (c, b) } is: a. reflexive, antisymmetric, symmetric b. transitive, symmetric, antisymmetric c. antisymmetric, reflexive, transitive d. symmetric, reflexive, transitive
(Please Show all work)A relation R is defined on Z by aRb if 7x−5y is even....
(Please Show all work)A relation R is defined on Z by aRb if 7x−5y is even. Show that R is an equivalence relation.
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 A = R x R, and let a relation S be defined as: “(x1 ,...
Let A = R x R, and let a relation S be defined as: “(x1 , y1 ) S (x2 , y2 ) ⬄ points (x1 , y1 ) and (x2 , y2 ) are 5 units apart.” Determine whether S is reflexive, symmetric, or transitive. If the answer is “yes,” give a justification (full proof is not needed); if the answer is “no” you must give a counterexample