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4. Give the directed graph of a relation on the set ( x,y,z that is a)...
Let X, be the set {x € Z|3 SXS 9} and relation M on Xz defined...
Let X, be the set {x € Z|3 SXS 9} and relation M on Xz defined by: xMy – 31(x - y). (Note: Unless you are explaining “Why not,” explanations are not required.) a. Draw the directed graph of M. b. Is M reflexive? If not, why not? C. Is M symmetric? If not, why not? d. Is M antisymmetric? If not, why not? e. Is M transitive? If not, why not? f. Is M an equivalence relation, partial order...
Let A = { 1, 2, 3, 4, 5 }. Give examples of a relation over...
Let A = { 1, 2, 3, 4, 5 }. Give examples of a relation over AxA that has exactly 5 elements that satisfy each of the following properties: Reflexive: Irreflexive: Symmetric: Antisymmetric: Transitive:
3. (12 pts) Determine whether the following binary relation is: (1) reflexive, (2) symmetric, (3) antisymmetric,...
3. (12 pts) Determine whether the following binary relation is: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive. a) The relation Ron Z where aRb means a = b. Circle your answers. (4 pts) Ris Reflexive? Symmetric? Antisymmetric? Transitive? Yes or No Yes or No Yes or No Yes or No b) The relation R on the set of all people where aRb means that a is taller than b. Circle your answers. (4 pts) Ris Reflexive? Symmetric? Antisymmetric? Transitive?...
Let z denote a complete, reflexive and transitive weak preference relation over a set X, and...
Let z denote a complete, reflexive and transitive weak preference relation over a set X, and let > denote the strict preference relations derived from 2. Select one: O a. the strict preference relation is neither transitive nor complete. O b. the strict preference relation is both transitive and complete. c. the strict preference relation is transitive but not necessarily complete. O d. the strict preference relation is complete but not necessarily transitive.
Given the following binary relations: The relation Rl on {w, 1, y, z), where R1 =...
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?
Determine whether the relation R on the set of all real numbers is reflexive, symmetric,...
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
10. Represent the following relation R on the set (. t,s t) as a digraph and...
10. Represent the following relation R on the set (. t,s t) as a digraph and as a acro-ooe ati eachi b) Circle the properties of R antisymmetric itive 2 peins) reflexive symmetric 떼 1 find the symmetric and transitive closures ofS (4 pirtepi 1 c)If Ms-10 Transitive Closure Symmetric Closure_-
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...
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)...
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,...
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,...
(5 pts) Give an example of a relation on a set that is a) both symmetric...
(5 pts) Give an example of a relation on a set that is a) both symmetric and antisymmetric. b) neither symmetric nor antisymmetric. (3 pts each) For each of the following find an indexed collection {An}nen of distinct sets (no two sets are equal) such that (a) n =1 An = {0} (b) Um_1 An = [0, 1] (c) n =1 An = {-1,0,1} (5 pts each) Give example of an explicit function f in each of the following category...
Let X, be the set {x € Z|3 SXS 9} and relation M on Xz defined by: xMy – 31(x - y). (Note: Unless you are explaining “Why not,” explanations are not required.) a. Draw the directed graph of M. b. Is M reflexive? If not, why not? C. Is M symmetric? If not, why not? d. Is M antisymmetric? If not, why not? e. Is M transitive? If not, why not? f. Is M an equivalence relation, partial order...
3. (12 pts) Determine whether the following binary relation is: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive. a) The relation Ron Z where aRb means a = b. Circle your answers. (4 pts) Ris Reflexive? Symmetric? Antisymmetric? Transitive? Yes or No Yes or No Yes or No Yes or No b) The relation R on the set of all people where aRb means that a is taller than b. Circle your answers. (4 pts) Ris Reflexive? Symmetric? Antisymmetric? Transitive?...
Let z denote a complete, reflexive and transitive weak preference relation over a set X, and let > denote the strict preference relations derived from 2. Select one: O a. the strict preference relation is neither transitive nor complete. O b. the strict preference relation is both transitive and complete. c. the strict preference relation is transitive but not necessarily complete. O d. the strict preference relation is complete but not necessarily 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?
10. Represent the following relation R on the set (. t,s t) as a digraph and as a acro-ooe ati eachi b) Circle the properties of R antisymmetric itive 2 peins) reflexive symmetric 떼 1 find the symmetric and transitive closures ofS (4 pirtepi 1 c)If Ms-10 Transitive Closure Symmetric Closure_-
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)...
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,...
(5 pts) Give an example of a relation on a set that is a) both symmetric and antisymmetric. b) neither symmetric nor antisymmetric. (3 pts each) For each of the following find an indexed collection {An}nen of distinct sets (no two sets are equal) such that (a) n =1 An = {0} (b) Um_1 An = [0, 1] (c) n =1 An = {-1,0,1} (5 pts each) Give example of an explicit function f in each of the following category...
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