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Check which of the following options are TRUE for the relation R* The relation R is...
Math 240 Assignment 4 - due Friday, February 28 each relation R defined on the given set A, determine whether or not it is reflexive, symmetric, anti-symmetric, or transitive. Explain why. (a) A = {0, 1,2,3), R = {(0,0).(0,1),(1,1),(1,2).(2, 2), (2.3)} (b) A = {0, 1,2,3), R = {(0,0).(0,2), (1,1),(1,3), (2,0), (2,2), (3,1),(3,3)} (c) A is the set of all English words. For words a and b, (a,b) E R if and only if a and b have at least...
[Partial Orders - Six Easy Pieces] A binary relation is R is said to be antisymmetric if (x,y) ER & (y,x) ER = x=y. For example, the relations on the set of numbers is antisymmetric. Next, R is a partial order if it is reflexive, antisymmetric and transitive. Here are several problems about partial orders. (a) Let Ss{a,b} be a set of strings. Let w denote the length of the string w, i.e. the number of occurrences of letters (a...
Question 17 5 pts Let the relation Ron {1,2,3} be given by the following table: R 1 2 3 3 X X X Check all properties that this relation has transitive symmetric reflexive anti-symmetric
1. Define a relation on Z by aRb provided a -b a. Prove that this relation is an equivalence relation. b. Describe the equivalence classes. 2. Define a relation on Z by akb provided ab is even. Use counterexamples to show that the reflexive and transitive properties are not satisfied 3. Explain why the relation R on the set S-23,4 defined by R - 11.1),(22),3,3),4.4),2,3),(32),(2.4),(4,2)) is not an equivalence relation.
Question 2 For each of the following relations R, determine (and explain) whether R is: (1) reflexive (2) symmetric (3) antisymmetric (4) transitive (a) R-(x, y):x +2y 3), defined on the set A 10, 1,2,3) (b) R-I(x, y): xy 4), defined on the set A (0,1,2,3,4 (c) R-(x, y): xy 4), defined on the set A-0,,2,3) Question 2 For each of the following relations R, determine (and explain) whether R is: (1) reflexive (2) symmetric (3) antisymmetric (4) transitive (a)...
8. On the set A = {1,2,3,4,...,20}, an equivalence relation R is defined as follows: For all x, y € A, xRy 4(x - y). For each of the following, circle TRUE or FALSE. [4 points) a. TRUE or FALSE: There are only 4 distinct equivalence classes for this relation. b. TRUE or FALSE: If you remove all the even numbers from A, the relation would still be an equivalence relation. C. TRUE or FALSE: In this equivalence relation, 2R5...
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,...
Let R be a relation defined on the integers Z by a R b if 6b^3 - 6a^3 <= 0 Which of the properties reflexive, symmetric, and transitive does R possess?
(4) (a) Give an example of a relation (different to those in question 1) which is symmetric and transitive but not reflexive. (b) Identify the problem with the following proof: Let R be a relation on a set S, and suppose that R is symmetric and transitive. Since the relation is symmetric, we know that a bb~a, and then it follows from transitivity that a ~b and b ~ a → a ~ a. Therefore any symmetric and transitive relation...
Relations - No Proofs! Determine (no proof needed!) whether each of the following relations R, S, T on the set of real numbers is reflexive, symmetric, antisymmet- ric, and/or transitive. a) « Ry iff r - y is positive: reflexive: symmetric: anti-symmetric: transitive: b) Sy iff r = 2y reflexive: symmetric: anti-symmetric: transitive: c) <Ty iff zy < 0: reflexive: symmetric: anti-symmetric: transitive: