3. (12 pts) Determine whether the following binary relation is: (1) reflexive, (2) symmetric, (3) antisymmetric,...
Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if a) x + y = 0 b) x= ±y. c) x-y is a rational number. d) = 2y. e) xy ≥ 0. f) xy = 0. g) x=l. h) r=1 or y = 1
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)...
Question 8 4 pts A relation Rfrom a set A to a set Bis a subset of а. А х А b. Вх В с. Ах В d. B x A d. Question 9 4 pts A relation Ron a set A is an equivalence relation if either of the following is true: (a) Ris reflexive on A (b) Ris symmetric on A (c) Ris transitive on A. True False
Please explain in detail!! 4. If binary relation R is given by matrix [1 0 1 0 1 101 м, 1 1 1 0 1 1 0 1 determine, if R is: (a) reflexive (b) symmetric (c) antisymmetric (d) transitive?
Given the following binary relations: The relation Rl on {w, 1, y, z), where R1 = {(w, w), (w, 1), (x, w), (x, 1 ), (x, z), (y, y), (z,y),(2, 2)). The relation R2 on (a, b, c), where R2 = {(a, a ), (b, b), (c, c), (a, b), (a, c), (c, b)}. The relation R3 on {x,y,z}, where R3 = {(1, 2), (9,2), (2, y)}. Determine whether these relations are: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive?
[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...
2. (15 points) For each relation, indicate whether the relation is: • reflexive, anti-reflexive, or neither • symmetric, anti-symmetric, or neither transitive or not transitive a. (5 pts) 1 1 1 1 1 O 1 2 1 1 0 0 3 1 0 0 1 4 0 0 0 0 b. (5 pts) 1 0 1 1 0 2 1 0 0 0 3 1 0 0 1 4 0 0 1 0 4 c. (5 pts) 1 1 0...
Suppose that R61,3), (1, 4), (2, 3), (2,4), (3,1), (3,4)), Determine which of these statements are correct Check ALL correct answers below A. R6 is symmetric B. R1 is reflexive C. R4 is symmetric D. R3 is transitive E. R3 is reflexive F. R2 is reflexive G. R2 is not transitive H. R4 is antisymmetric I. R1 is not symmetric J. R5 is transitive K. R4 is transitive L. Rs is not reflexive M. R3 is symmetric
For each of the following relations, determine whether it is reflexive, anti-reflexive, symmetric, anti-symmetric, or transitive. Briefly explain your answers for each one. (a) (2 points) The domain is all CPUs. For any CPUs x and y, xRy if x has at least as many cores as y. (b) (2 points) The domain is all people. For any people x and y, xRy if x and y are friends. Assume that everyone is his/her own friend, and that if A...
discrete maths 2. (Lewis, Zar 14.7) Determine whether each of the following relations is transitive, symmetric, and reflexive and why: (a) The subset relation (b) The proper subset relation (c) The relation R on Z, where R(a, b) if and only if b is a multiple of a (d) The relation R on ordered pairs of integers, where R(<a,b>,<c,d >) if and only if ad-bc.