Consider the relation R on N such that xRy if and only if the sum of...

Consider the relation R on N such that xRy if and only if the sum of the digits of x and y coincide.

(i) Prove or disprove R is an equivalence relation. (ii) What are the equivalence classes of R.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Consider the relation R defined on the set Z as follows: ∀m, n ∈ Z, (m,...

Consider the relation R defined on the set Z as follows: ∀m, n ∈ Z, (m, n) ∈ R if and only if m + n = 2k for some integer k. For example, (3, 11) is in R because 3 + 11 = 14 = 2(7). (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.

Consider the following recurrence relation defined only for n = 2^k for integers k such that...

Consider the following recurrence relation defined only for n = 2^k for integers k such that k ≥ 1: T(2) = 7, and for n ≥ 4, T(n) = n + T(n / 2). Three students were working together in a study group and came up with this answer for this recurrence: T(n) = n * log2 (n) − n − log2 (n) + 8. Determine if this solution is correct by trying to prove it is correct by induction.

Define a relation S from R to R by saying that if and only if (a) List...

Define a relation S from R to R by saying that if and only if (a) List five different elements of S. (b) Prove that S is not a function.

Show that the relation 'a R b if and only if a−b is an even integer defined on the Z of integers is an equivalence relation.

Consider the following recursive algorithm for computing the sum of the first n squares: S(n) =...

Consider the following recursive algorithm for computing the sum of the first n squares: S(n) = 12 +22 +32 +...+n2 . Algorithm S(n) //Input: A positive integer n //Output: The sum of the first n squares if n = 1 return 1 else return S(n − 1) + n* n a. Set up and solve a recurrence relation for the number of times the algorithm’s basic operation is executed. b. How does this algorithm compare with the straightforward non-recursive algorithm...

Assume A = R and the relation R ⊆ A × A such that for x,...

Assume A = R and the relation R ⊆ A × A such that for x, y, ∈ R, xRy if and only if sin2 x + cos2 y = 1. Prove that R is an equivalence relation and for any fixed x ∈ R, find the equivalence class x

Question: Consider the relation R on A defined by aRb iff 1mod4 = bmod4 a)Construct the...

Question: Consider the relation R on A defined by aRb iff 1mod4 = bmod4 a)Construct the diagraph for this relation b)show that R is an equivalence relation Part B: Now consider the relation R on A defined by aRb iff a divides b (Divides relation) c) Show that R is partial ordering d) Contruct the hasse diagram for this relation

Consider a relation R (ABCDEFGH) with the following functional dependencies: ACD --> EF AG --> A...

Consider a relation R (ABCDEFGH) with the following functional dependencies: ACD --> EF AG --> A B --> CFH D --> C DF --> G F --> C F --> D Find minimal cover and identify all possible candidate keys. In order to receive full credit, please list each step taken and the rules that you applied.

Question 1. Equivalence Relation 1 Define a relation R on by iff . Prove that R...

Question 1. Equivalence Relation 1 Define a relation R on by iff . Prove that R is an equivalence relation, that is, prove that it is reflexive, symmetric, and transitive. Determine the equivalence classes of this relation. What members are in the class [2]? How many members do the equivalence classes have? Do they all have the same number of members? How many equivalence classes are there? Question 2. Equivalence Relation 2 Consider the relation from last week defined as:...

Consider the given function. Evaluate the Riemann sum for 0 ≤ x ≤ 3, with n...

Consider the given function. Evaluate the Riemann sum for 0 ≤ x ≤ 3, with n = 6, taking the sample points to be right endpoints.

Subjects