Question

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

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 the set of all lines in the plane. Let the relation R be...
Let A be the set of all lines in the plane. Let the relation R be defined as: “l​1​ R l​2​ ⬄ l​1​ intersects l​2​.” 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.
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?
Let A be the set of all integers, and let R be the relation "m divides...
Let A be the set of all integers, and let R be the relation "m divides n." Determine whether or not the given relation R, on the set A, is reflexive, symmetric, antisymmetric, or transitive.
Let A be the set of all real numbers, and let R be the relation "less...
Let A be the set of all real numbers, and let R be the relation "less than." Determine whether or not the given relation R, on the set A, is reflexive, symmetric, antisymmetric, or transitive.
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,
Consider the following relation on the set Z: xRy ? x2 + y is even. For...
Consider the following relation on the set Z: xRy ? x2 + y is even. For each question below, if your answer is "yes", then prove it, if your answer is "no", then show a counterexample. (i) Is R reflexive? (ii) Is R symmetric? (iii) Is R antisymmetric? (iv) Is R transitive? (v) Is R an equivalence relation? If it is, then describe the equivalence classes of R. How many equivalence classes are there?
Determine whether the relation R is reflexive, symmetric, antisymmetric, and/or transitive [4 Marks] 22 The relation...
Determine whether the relation R is reflexive, symmetric, antisymmetric, and/or transitive [4 Marks] 22 The relation R on Z where (?, ?) ∈ ? if ? = ? . The relation R on the set of all subsets of {1, 2, 3, 4} where SRT means S C T.
Let X,Y be posets. Define a relation ≤ on X × Y by the reciepe:                ...
Let X,Y be posets. Define a relation ≤ on X × Y by the reciepe:                 (x1,y1) ≤(x2,y2) iff   x1 ≤ x2     in X   and y1 ≤ y2 in Y In Above example check that (X ×Y,≤) is actually a poset, It is the product poset of X and Y
Let A = {1,2,3,4,5} and X = P(A) be its powerset. Define a binary relation on...
Let A = {1,2,3,4,5} and X = P(A) be its powerset. Define a binary relation on X by for any sets S, T ∈ X, S∼T if and only if S ⊆ T. (a) Is this relation reflexive? (b) Is this relation symmetric or antisymmetric? (c) Is this relation transitive?
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...