Homework Answers
2) REFLEXIVE: (x,x) does not belongs to S(x,y) because x can not be brother or sister of himself/herself. so S(x,y) is not reflexive.
SYMMETRIC:if (x,y) belongs to S(x,y) then x is brother or sister of y. that means y is also brother or sister of x and hence (y,x) also belongs to S(x,y). Therefore given relation is symmetric.
TRANSITIVE: let (x,y) and (y,x) belongs to S(x,y) then (x,x) does not belongs to S(x,y) as x can not be brother or sister of himself/herself. so given relation is not transitive.
S is not an equivalence relation as it is not reflexive and transitive.
3)R={(a,a),(b,b),(c,c),(d,d),(a,b),(a,c),(a,d),(b,a),(b,c),(b,d),(c,a),(c,b),(c,d),(d,a),(d,b)(d,c)}
There are 16 elements in above relation. These are the largest number possible for equivalence relation on given set A
Add Answer to:
Can you #2 and #3? 6. LESSON 6 (1) Let A be the set of people alive on earth. For each relation defined below, determin...
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,...
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...
probelms 9.1 9 Modular arithmetic Definition 9.1 Let S be a set. A relation R =...
probelms 9.1
9 Modular arithmetic Definition 9.1 Let S be a set. A relation R = R(,y) on S is a statement about pairs (x,y) of elements of S. For r,y ES, I is related to y notation: Ry) if R(x,y) is true. A relation Ris: Reflexive if for any I ES, R. Symmetric if for any ry ES, Ry implies y Rr. Transitive if for any r.y.ES, Ry and yRimply R. An equivalence relation is a reflexive, symmetric and...
discrete mathematics help 1. List the order pairs in the relation R from A ={0, 1,...
discrete mathematics help 1. List the order pairs in the relation R from A ={0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a, b) Î R if and only if a) a = b b) a + b = 4 c) a > b d) a|b //6th edition ((a), (b), (c), and (d) of Exercise 1, Page 527.) 2. a) List all the ordered pairs in the relation R = {(a, b) |a divides b}...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by (s, t) E< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element x is minimal if there does not exist y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give an example of a total order on...
Math 240 Assignment 4 - due Friday, February 28 each relation R defined on the given...
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...
Answer each question in the space below. 1. Let A = {0,1} U... U{0,1}5 and let...
Answer each question in the space below. 1. Let A = {0,1} U... U{0,1}5 and let be the order on A defined by (s, t) €< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element & is minimal if there does not erist Y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give...
I. Let each of R, S, and T be binary relations on N2 as defined here: R-[<m, n EN nis the smallest prime number greater than or equal to m] S -[< m, n> EN* nis the greatest prime number less...
I. Let each of R, S, and T be binary relations on N2 as defined here: R-[<m, n EN nis the smallest prime number greater than or equal to m] S -[< m, n> EN* nis the greatest prime number less than or equal to m] (a) Which (if any) of these binary relations is a (unary) function? (b) Which (if any) of these binary relations is an injection? (c) Which (if any) of these binary relations is a surjection?...
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)...
Let R be the relation on the set {1, 2, 3} containing the ordered pairs (1, 1), (1, 2), (2, 3), (3, 1). Find a) R 2 b) R...
Let R be the relation on the set {1, 2, 3} containing the ordered pairs (1, 1), (1, 2), (2, 3), (3, 1). Find a) R 2 b) R 3 c) R 4 d) R 5 Consider the same relation R as above. List all walks in R staring from node 3 that correspond to the edges in a) R 2 b) R 3
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 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...
probelms 9.1
9 Modular arithmetic Definition 9.1 Let S be a set. A relation R = R(,y) on S is a statement about pairs (x,y) of elements of S. For r,y ES, I is related to y notation: Ry) if R(x,y) is true. A relation Ris: Reflexive if for any I ES, R. Symmetric if for any ry ES, Ry implies y Rr. Transitive if for any r.y.ES, Ry and yRimply R. An equivalence relation is a reflexive, symmetric and...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by (s, t) E< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element x is minimal if there does not exist y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give an example of a total order on...
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...
Answer each question in the space below. 1. Let A = {0,1} U... U{0,1}5 and let be the order on A defined by (s, t) €< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element & is minimal if there does not erist Y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give...
I. Let each of R, S, and T be binary relations on N2 as defined here: R-[<m, n EN nis the smallest prime number greater than or equal to m] S -[< m, n> EN* nis the greatest prime number less than or equal to m] (a) Which (if any) of these binary relations is a (unary) function? (b) Which (if any) of these binary relations is an injection? (c) Which (if any) of these binary relations is a surjection?...
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)...
Most questions answered within 3 hours.
-
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 8 minutes ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 7 minutes ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 13 minutes ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 21 minutes ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 16 minutes ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 17 minutes ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 21 minutes ago -
Would CuCO3 aqueous salt combined with calcium chloride
form a solid precipitate? If so, what would...
asked 20 minutes ago -
How do ECM Solutions assist in embedding a culture of continuous
improvement in an organization? (Project...
asked 40 minutes ago -
Directions
These directions introduce the idea of Essential Questions.
Since this may be a new concept...
asked 42 minutes ago -
1.b. Fiscal policy is said to suffer from ‘crowding out’.
Explain what this means and why...
asked 1 hour ago -
The equation for the reaction of nitrogen and oxygen to form
nitrogen oxide is written as...
asked 1 hour ago