(10) Define a relation R on Zn (the integers mod n) as follows: lal isR related...

Question

Question

(10) Define a relation R on Zn (the integers mod n) as follows: lal isR related to [b (i.e. [an Rbn) iff there is [cn E Gn su

Answer 1

Answer #1

Such that ata Tala So anequivalence elaher CaJn 170 012 lo 637,91

Answer 2

Similar Homework Help Questions

(14) Let R be a relation on the integers defined by m R n if and...

(14) Let R be a relation on the integers defined by m R n if and only if m+m2 n+ n2(mod 5). Show that R is an equivalence relation and determine all the equivalence classes.
probelms 9.1 9 Modular arithmetic Definition 9.1 Let S be a set. A relation R =...

probelms 9.1 9 Modular arithmetic Definition 9.1 Let S be a set. A relation R = R(,y) on S is a statement about pairs (x,y) of elements of S. For r,y ES, I is related to y notation: Ry) if R(x,y) is true. A relation Ris: Reflexive if for any I ES, R. Symmetric if for any ry ES, Ry implies y Rr. Transitive if for any r.y.ES, Ry and yRimply R. An equivalence relation is a reflexive, symmetric and...
Let R be the relation defined on Z (integers): a R b iff a + b...

Let R be the relation defined on Z (integers): a R b iff a + b is even. Then the distinct equivalence classes are: Group of answer choices [1] = multiples of 3 [2] = multiples of 4 [0] = even integers and [1] = the odd integers all the integers None of the above

9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff...

9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc (a) R is symmetric but not reflexive. (b) R is transitive and symmetric but not reflexive (c) R is reflexive and transitive but not symmetric (d) None of the above 10. Let R be an equivalence relation on a nonempty and finite 9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc...
(b) Let be the relation on N define by a ~ b iff there are m,n...

(b) Let be the relation on N define by a ~ b iff there are m,n e Z+ with albm and bla". Show that is an equivalence relation. on hea infinitolo
2. Let f : A ! B. DeÖne a relation R on A by xRy i§ f (x) = f (y). a. Prove that R is an equivalence relation on A. b. Let Ex = fy 2 A : xRyg be the equivalence class of x 2 A. DeÖne E = fEx : x 2 Ag...

2. Let f : A ! B. DeÖne a relation R on A by xRy i§ f (x) = f (y). a. Prove that R is an equivalence relation on A. b. Let Ex = fy 2 A : xRyg be the equivalence class of x 2 A. DeÖne E = fEx : x 2 Ag to be the collection of all equivalence classes. Prove that the function g : A ! E deÖned by g (x) = Ex is...

Discrete Math. Show all steps clearly Define a relation R on the set of all integers...

Discrete Math. Show all steps clearly Define a relation R on the set of all integers Z as follows: Is R a partial order relation? Prove or give a counterexample.
Problem 3. (20 points) Define a relation among the functions that map from N to R+...

Problem 3. (20 points) Define a relation among the functions that map from N to R+ as follows: f(n) g(n) iff f (n) is o(g(n)) i.e. f(n) is O(gfn) but g(n) is not O(f(n)). Order the following functions according to <assuming e is a real constant, 0<E<1. Provide justifcations for your answer. (a) n log n, ( e), and (h) (1/3)" ni+e, (e) (n Problem 4. (15 points) Solve the following recurrence equations and give the solution in θ notation;...
6. Fix n E N and recall the definition of the equivalence relation on Z given...

6. Fix n E N and recall the definition of the equivalence relation on Z given by a = b mod n. (This means that a – b = kn, for some k € Z.) Let [a] denote the equivalence class containing a. (a) Show that defining [a] + [b] := (a + b] makes sense, i.e. does not depend on the choice of representatives for the classes. (b) Show that defining [a] × [b] := [a x b] makes...

[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on...

[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on A x A by: for any (a,b), (c,d) E AXA, (a,b) R (c,d) if and only if a +b=c+d. (a) Prove that R is an equivalence relation on AX A. (b) List all the elements of [(3,3)], the equivalence class of (3, 3). (c) How many equivalence classes does R have? Explain. (d) Is there an equivalence class that has exactly 271 elements? Explain.