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.

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

Q: Thoorem: is not closed set

A:

Q: Suppose f function between infinite sets A and B, f is not onto function, does the sets A and B have…

A: Yes. It is possible that A and B have same cardinality. Let A and B both are the set of natural…

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

A:

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: 4. Let A = {1,2,3,4). Find a non-empty relation on set A such that the given MI conditions are met,…

A:

Q: Prove that the relation of congruence is an equivalence relation.

A: A relation is said to be an equivalence relation if and only if the relation is reflexive, symmetric…

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: What property is NOT included for an EQUIVALENCE RELATION? * O Reflexive O symmetric O Transitive O…

A:

Q: Show that any 2-cut relation (for > 0) of a fuzzy equivalence relation results in a crisp…

A: Let's take the fuzzy relation: R = 10.800.10.20.810.400.900.41000.10010.50.20.900.51 Fuzzy tolerance…

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

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…

A:

Q: Show that the number of equivalence relation in the set {1, 2, 3} containing(1, 2) and (2, 1) is…

A: To show:The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two.

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…

A:

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, ∃∈&gt;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: 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…

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

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: Consider the relation R = {(a, b), (a, c), (c, b), (b, c)} on the set A = {a, b, c}. Is R reflexive,…

A:

Q: Construct a relation on the set {1,2,3,4} that is reflexive, antisym- metric, and not transitive.

A:

Q: Let S be a set of distinct symbols. Show that the relation defined onW(S) in this chapter is an…

A:

Q: Let R be a total relation on a set of 15 elements. Then the number of ordered pairs in R is equal…

A:

Q: A relation R, is defined on Z, the set of integers by aRb + a - b is even. Show that R is…

A:

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,…

A:

Q: Determine whether the relation R on the set of all integers defined by the rule (x,y) Î R if and…

A:

Q: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

A:

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…

A:

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 defined on the set Z by aRb if floor value of a = floor value of b. What…

A:

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

A:

Q: Show that any 1-cut relation (for 1> 0) of a fuzzy equivalence relation results in a crisp…

A: Consider the fuzzy relation: R =10.800.10.20.810.400.900.4100010010.50.20.900.51 Fuzzy tolerance…

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: Sketch a digraph for a relation on the set {a, b, c, d} that is irreflexive and symmetricbut not…

A: Denote R by the relation on the set S={a, b, c, d} that is irreflexive, symmetric and not…

Q: Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3),(4,5)} on the set A =…

A: Let R be a binary relation on a set A. R is said to be  reflexive if for all . R is said to be…

Q: Define a relation ~ on the set of real numbers by X~ y means | x |+|y|=|x+y|. Determine whether - is…

A:

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,…

A:

Q: In the set A = {1, 2, 3, 4} is defined a relation R by %3D R = {(1, 1), (1, 3), (3, 4), (4, 3)}.…

A: Given set is A = {1, 2, 3, 4}  with relation R = {(1, 1), (1, 3), (3, 4), (4, 3)}

Q: Find the number of different partions of a set (a) with one element (b) with two elements (c)…

A:

Q: Define a relation on the set {a, b, c, d} that is (a) irreflexive and transitive, but not symmetric.…

A:

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,…

A:

Q: Let R be the relation on the set of all people who have visited a particular Web page such that x Ry…

A: Given

Q: Let S be a nonempty set. Consider the relation ~ on P(S) defined byA ~ B if A U BC = S. Is the…

A: Let S be a nonempty set. Consider the relation ~ on P(S)  defined by A~B if A∪Bc=S To show: "~" is…

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: What is equivalence relation

A: For a set A, a relation R defined on A is called EQUIVELENCE RELATION, if it is REFLEXIVE, SYMMETRIC…

Q: What is the possible number of reflexive relations on a set of 5 elements?

A: Introduction : We have give a set of 5 elements , we have asked for the number of reflexive…

Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

A: Given: Let A be a non-empty set let~ be a relation on ℘(A) Let "A" be a non-empty set Let ~ be a…

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