Determine if {(x,y) | x divides 2-y} is an equivalence relation on {1,2,3,4,5}. List the equivalence...
- 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 people
List the members of the equivalence relation on {1,2,3,4}. Find the equivalence classes [1],[2],[3],[4] for the following:
- {{1,2},{3,4}}
- {{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
Homework Answers
- Determine if {(x,y) | x divides 2-y} is an equivalence relation on {1,2,3,4,5}. List the equivalence classes
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Determine if {(x,y) | x divides 2-y} is an equivalence relation
on {1,2,3,4,5}. List the equivalence...
List the members of the equivalence relation on {1,2,3,4}. Find the equivalence classes [1],[2],[3],[4] for the...
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 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
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)...
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2),...
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4,4), (4,5), (5,4), (5,5)} Given that R is an equivalence relation on A, which of the following is the partition of A into equivalence classes? Select the correct response. A. P = {{1}, {1, 2}, {3}, {3,4}, {4},{5}} B. P ={{1,2,3,4,5}} C. P ={{1,2},{3,4}, {5}} D. P = {{1}, {2,3}, {4,5}} E. P ={{1,2,3}, {1,5}} F. P= {{1},...
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...
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?...
8. On the set A = {1,2,3,4,...,20}, an equivalence relation R is defined as follows: For...
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...
QUESTION 30 Let R be the relation on the set A={1,2,3,4,5} given by R={(x,y): y=x+2}. What...
QUESTION 30 Let R be the relation on the set A={1,2,3,4,5} given by R={(x,y): y=x+2}. What is the size of RoR? QUESTION 31 How many relations on the set {4,5} are reflexive? QUESTION 32 How many relations on the set {4,5} are not reflexive?
Let R be the relation on N defined by xRy iff 2 divides x+y. R is...
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.
4) Determine whether the following relation is an equivalence relation. Justify your answer. If the relation...
4) Determine whether the following relation is an equivalence relation. Justify your answer. If the relation is an equivalence relation, then describe the partition defined by the equivalence classes. The domain is a group of people. Person x is related to person y under relation M if x and y have the same biological mother. You can assume that there is at least one pair in the group, x and y, such that xMy.
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)...
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4,4), (4,5), (5,4), (5,5)} Given that R is an equivalence relation on A, which of the following is the partition of A into equivalence classes? Select the correct response. A. P = {{1}, {1, 2}, {3}, {3,4}, {4},{5}} B. P ={{1,2,3,4,5}} C. P ={{1,2},{3,4}, {5}} D. P = {{1}, {2,3}, {4,5}} E. P ={{1,2,3}, {1,5}} F. P= {{1},...
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?...
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...
QUESTION 30 Let R be the relation on the set A={1,2,3,4,5} given by R={(x,y): y=x+2}. What is the size of RoR? QUESTION 31 How many relations on the set {4,5} are reflexive? QUESTION 32 How many relations on the set {4,5} are not reflexive?
4) Determine whether the following relation is an equivalence relation. Justify your answer. If the relation is an equivalence relation, then describe the partition defined by the equivalence classes. The domain is a group of people. Person x is related to person y under relation M if x and y have the same biological mother. You can assume that there is at least one pair in the group, x and y, such that xMy.
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