Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary subsets of A, B~C iff B⊆C. What kind of order is ~ (if any)? Prove the properties that hold, and construct counterexamples for the properties that don't

Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary subsets of A, B~C iff B⊆C. What kind of order is ~ (if any)? Prove the properties that hold, and construct counterexamples for the properties that don't

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

See similar textbooks

Related questions

Q: Let A = (1, 2, 3, 4, 6). Let Ri be a relation defined on A. a. Verify reflexive property on the…

A: "Hi! Thank you for the question! Since the question contains four subparts and we are allowed to…

Q: Let A = {1, 2, 3, 4, 6}. Let Ri be a relation defined on A. a. Verify reflexive property on the…

Q: If R ={ (1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} is a relation on {1, 2, 3, 4}. Find the reflexive…

Q: Let a relation S be defined on A = {0, 1, 2, 3} as follows. S= {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

Q: disprove: a relation that is symmetric and transitive must TProve also be reflexive. or

Q: Give an example of a relation on the set {a, b, c, d} which is symmetric and transitive, but not…

A: Any relation R from a set Ato A is reflexive if and only if for every x∈A , the pair (x,x)∈R Any…

Q: A ° = A – JA

Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,b),(b,b),(b,c)(c,a)(c,c) and…

A: Given set is A = {a, b, c, d} and the relation R on set A is R = {(a, b), (b, b), (b, c), (c, a),…

Q: Identify the relation on set (1,2,3,4} if it is reflexive, symmetric, antisymmetric or transitive.…

A: We know that , relation is relationship between sets of values. A binary relation R defined on set A…

Q: Let A = {1, 2, 3, 4}. Let R be the relation on A defined as follows: R = {(1, 1), (1, 2),…

Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R symmetric? Is it…

A: R=1,2,2,1,2,3,3,4,4,1set=1,2,3,4

Q: Use the Heine-Borel theorem to give an example of a set not compact in R with the usual topology…

A: An example of a set not compact in R with the usual topology and a non-compact set R2 with the usual…

Q: Show that the relation R = ∅ on a nonempty set S is symmetric and transitive, but not reflexive

A: See the attachment.

Q: A relation ''<'' is 1) İrreflexive. 2) Transitive. called a quasi-order on a set S if its: صواب ihi

A: We know that

Q: let A be the relation on the set integers defined by s A t if and only if |a| <= |t| is the…

Q: Let R be a relation over a set A = {a,b,c,d}. What kind of order is R? Note: Select the order that…

Q: Give an example of a closed set in R ^ 3 with the usual topology that is not compact

A: Given the usual topology on ℝ3. i.e. τusual=U⊆ℝ3: ∀x∈U, ∃∈>0 such that B∈x⊆U

Q: Let D be the relation on the natural numbers defined by the rule m divides n if and only if m does…

A: Let D be the relation on the natural number is defined by the rule m divides n if an only if m does…

Q: A relation R on a set S is said to be transitive ifffor all x, y, z ∈R, xRy ∧ yRz ⇒ xRz. Relation R…

A: It is given that A relation R on a set S is said to be transitive ifffor all x, y, z ∈R, xRy ∧ yRz ⇒…

Q: Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on the set {1,…

Q: Determine whether the relation R on the set of all people is reflexive,symmetric, antisymettric…

A: Consider the provide question,

Q: Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric,…

Q: Let R be the relation on the set S = {1,2, 3, a, b, c} given by xRy if and only if (x, y) E {(a, a),…

A: S=1,2,3,a,b,c To find: (a) , (b) , (c).

Q: Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and…

Q: Let A = {1, 2, 3, 4} and R a relation on A whose matri: 1 0 1 0 0 1 0 1 is Mr = 0 0 1 1 0 0 1…

Q: Determine whether the relation is reflexive, symmetric, antisymmetric and transitive. Provide one…

Q: Prove that closed balls are closed sets in the standard topology on R?.

A: Topology Question

Q: Let R be the relation on the set {1,2,3,4} containing th (1,2), (1,4), (2,1), (2,2), (2,3), (3,1),…

Q: Let R be the relation on the set S = {1,2,3, a, b, c} given by xRy if and only if (а, у) € {(а, а),…

A: Given R be the relation on the set S=1,2,3,a,b,c given by…

Q: 2|A:k||2|| Bx:||2) < || |||B||F k%3D1

A: Please check the answer in next step

Q: Define a relation S from R to R as follows:…

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

Q: Let X be a set equipped with the finite complement topology show X is compact Show that X is…

Q: Let A- {#, 7, x} and let R be the relation on. A given by R {(7, 7). (#, #)}. Prove or disprove…

A: Transitivity is a property of verbs that relates to whether a verb can take objects and how many…

Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

Q: Suppose that fis a function from A to B, where A and B are finite sets with |A|=|B|. Then fis…

A: We can solve this using definition of one to one and onto

Q: Let R be a relation from X to Y and S be its reverse relation from Y to X. Prove or disprove that R…

A: According to the given information it is required to prove/disprove that R is injective and well…

Q: Let R be a relation defined on the set Z by aRb if floor value of a = floor value of b. What…

Q: Use a particular counterexample to explain why R fails to be an equivalence relation is the…

A: We take counter example 9R10,10R11⇒9R 11

Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

Q: Show that the relation R in the set {1,2,3} given by R = {(1, 1), (2, 2),(3, 3), (1, 2), (2, 3)} is…

Q: Let RC R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given problem is :

Q: Let R be a relation from set A to B, if R is symmetric then its inverse will be...... Answer (Please…

A: Given R is a relation from set A to B. Let R is symmetric relation and R-1 be the inverse relation…

Q: Determine whether or not the relation R on the set of all people is reflexive, symmetric,…

Q: Find the transitive closure of the relation R={(1,2),(2,2), (2,3),(3,3)} on the set A=(1,2,3}.…

Q: Let X be infinite set and x0 ∈ X. Consider the topology τ = {G ⊆ X : x0 ∈ G or G = ∅} on X. Is (X, τ…

Q: Suppose R is a relation defined on the set A = {1, 2, 3}. If R = {(1,1), (1, 2), (2, 1), (2, 2), (3,…

Q: Let R be a relation on {a, b, c, d}) defined as R = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c),…

A: Concept:

Q: Let the relation R be {(1,2), (2,9), (5,6)}. Is R transitive? Give the reason.

A: Given : 1,2, 2,9, 5,6

Question

Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by:
Letting B and C be arbitrary subsets of A, B~C iff B⊆C.

What kind of order is ~ (if any)? Prove the properties that hold, and construct counterexamples for the properties that don't. Prove for irreflexive, and Connex as well.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.
Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
Let (A) be the power set of the nonempty set A, and let C denote a fixed subset of A. Define R on (A) by xRy if and only if xC=yC. Prove that R is an equivalence relation on (A).
29. Suppose , , represents a partition of the nonempty set A. Define R on A by if and only if there is a subset such that . Prove that R is an equivalence relation on A and that the equivalence classes of R are the subsets .
A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.
13. Consider the set of all nonempty subsets of . Determine whether the given relation on is reflexive, symmetric or transitive. Justify your answers. a. if and only if is subset of . b. if and only if is a proper subset of . c. if and only if and have the same number of elements.