8. On the set A = {1,2,3,4,...,20}, an equivalence relation R is defined as follows: For...
QI. Let A-(-4-3-2-1,0,1,2,3,4]. R İs defined on A as follows: For all (m, n) E A, mRn㈠4](rn2_n2) Show that the relation R is an equivalence relation on the set A by drawing the graph of relation Find the distinct equivalence classes of R. Q2. Find examples of relations with the following properties a) Reflexive, but not symmetric and not transitive. b) Symmetric, but not reflexive and not transitive. c) Transitive, but not reflexive and not symmetric. d) Reflexive and symmetric,...
List the members of the equivalence relation on {1,2,3,4}. Find the equivalence classes [1],[2],[3],[4] for the followi {{1},{2},{3},{4}} Determine whether each relation is reflexive,antisymmetric , or transitive (x,y) in R if xy>1 (x,y) in R if x > y (x,y) in R if 3 divides x + 2y
Determine if {(x,y) | x divides 2-y} is an equivalence relation on {1,2,3,4,5}. List the equivalence classes Determine if {(x,y) | x and y are both even or x and y are both odd} is an equivalence relation on {1,2,3,4,5}. List the equivalence classes. Determine if {(x,y) | x and y are the same height} is an equivalence relation on all people Determine if {(x,y) | x and y have the same color hair} is an equivalence relation on all...
10. [12 Points) Properties of relations Consider the relation R defined on R by «Ry x2 - y2 = x - y (a) Show that R is reflexive. (b) Show that R is symmetric. (c) Show that R is transitive. (d) You have thus verified that R is an equivalence relation. What is the equivalence class of 3? (e) More generally, what is the equivalence class of an element x? Use the listing method. (f) Instead of proving the three...
Write a function in python that takes a set A and a relation R(x, y) on A (as a python function such that R(x, y) returns true if and only if the relation xRy holds), and returns True if and only if the relation R is reflexive. Here is the function signature you need to use. def is reflexive(A, R): You can test your code as follows. s = {1,2,3} def y(x, y): return x == y def n(x, y):...
Let R be the relation on N defined by xRy iff 2 divides x+y. R is an equivalence relation. You do not have to prove that R is an equivalence relation. True or False: 3 ∈ 4/R.
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for all X, Y E P (s), (X, Y) E R if and only if IX-T] = IY-T]. (a) Prove that R is an equivalence relation. (b) How many equivalence classes are there? Explain. (c) How mauy elements of [ø], the equivalence class of ø, are there? Explain (d) How many elements of [f1,2,3, 4)], the equivalence class of (1,2,3,...
Let R be the relation defined on Z (integers): a R b iff a + b is even. R is an equivalence relation since R is: Group of answer choices Reflexive, Symmetric and Transitive Symmetric and Reflexive or Transitive Reflexive or Transitive Symmetric and Transitive None of the above
I. In each of the flbwing prdblems, the relation Bis defined in the set Z of all the integers. Say in eadh case if Ris: ne Reflexive Symmetnic 3 Antisymmetnic Transt ve Partial arder relotian 6) Equivalence relotion Justfy yaur a.xRy fondonly if x-2y b.xRy if ond only if X=-y c. xRy ifond only f X <Y d.xRy ifond anly if x2y e. xRy Ff and only if x-y-sk Pa any kez S onswer: I. In each of the flbwing...
Prove that the following relation R is an equivalence relation on the set of ordered pairs of real numbers. Describe the equivalence classes of R. (x, y)R(w, z) y-x2 = z-w2