34. Assume that is a nonempty set, every member of which is a transitive relation. (a) Is the set a transitive relation? (b) Is U a transitive relation?

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: In a relation, the set of outputs with respect to a rule is: * O piecewise. range. O domain. O…

A:

Q: Show that AB→C does not logically imply A→C, nor B→C.HINT: Write a relation instance that satisfies…

A:

Q: 5. Let S be the set of all the nonempty subsets of 2={a,b,c,d}. Define a relation R on S as follows:…

A: Any Relation is said to be equivalent if  it Reflexive , Symmetric and Transitive

Q: Construct the Hasse diagram for the “divides” relation, | on the set {2, 3, 4, 6, 8, 9, 12, 18}.…

A:

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

A:

Q: Draw the direction of the graph that represents the relations.

A: We need to draw the directed graph which is represented by the given relation,…

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: 1) Define a relation on the set of all people as follows: two persons x and y are related if and…

A: Reflexive: A relation is said to be reflexive, if (a, a) ∈ R, for every a ∈ A. Symmetric: A relation…

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9} and let R be the relation {(a,b) ! a , b} Find the smallest…

A:

Q: In the Axiom Systems section of the Background chapter (1.6), a binary relation <on a nonempty set X…

A: Given X is a set consisting of 64 teams.  Let ⩽ be the relation on X such that for a,b∈X, a≤b…

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

A:

Q: If S is a relation from a non-empty set A to a nonempty set B then

A: Solution :-

Q: 26. Use Algorithm 1 to find the transitive closures of these relations on {a, b, c, d, e}. a) {(a,…

A:

Q: let A= {a, b, c, d} and R= { (a,a), (a, c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. draw a…

A:

Q: 5. Determine whether the following relation is i) an equivalence relation ii) a partial ordering. R=…

A:

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

A:

Q: Which of the following relations is the Symmetric relation over the set A= {3,5,13}…

A:

Q: Which of the following sets of ordered pairs represents a relation that is not a funetion? (1, 1),…

A: We know that set of order pairs like (x,y) forms a relation. Now, when a relation contains a special…

Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: A relation R on a set A with elements a, b and c is said to be in a transitive relationship, then if…

Q: A relation that assigns to each element x from a set of inputs, or ________, exactly one element y…

A: To fill: The blanks of statement: Given: The statement is "A relation that assigns to each element x…

Q: Determine for the following relations on the set of people if the relation is an equiv- alence…

A: We have 4 relations in our hand. We need to decide whether they are An equivalence relation A…

Q: Q5) Let X = {a, b,c, d} and let R = { (a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (b, d), (d,…

A: Given : X = a, b, c, d R = a, a, a, b, a, c, b, a, b, b, b, c, b, d, d, d be a relation.   To show…

Q: A relation is an equivalence relation if it satisfies three properties. which of the following…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: 9.4. Let A = {a, b, c} and B = {1,2,3,4}. Then R1 = {(a, 2) , (a, 3) , (b, 1),(b,3), (c, 4)} is a…

A:

Q: Consider the relation R = {(a, a), (c, a), (b, c), (d, b)} then which of the following set…

A: We need to find R3 given R=a,a,c,a,b,c,d,b Now,  R2=RοRR3=RοR2=R2οR The composition of two…

Q: 7. Consider the following relations on the set A = {- -3, –5 – | R = {(-3, –3), (–3, –5), (-3, –7),…

A:

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

A:

Q: 2. Identify the sufficient condition in each of the following pairs: It is a consumer. It is a…

A:

Q: Let's generalize the situation in problem #1. Consider the relation < on the set [n] : {1,2,...,n}.…

A:

Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

A:

Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: Write down all of the properties that each of the following binary relations satisfies from among…

A: The objective is: (a) To write down all the properties for “has a common language with” relation on…

Q: 9.13. Let S = {a, b, c}. Then R= {(a,b)} is a relation on S. Which of the properties reflexive,…

A:

Q: Let A = {1,2,3,4}, B = {2,3,4,5}, and C = {2,4,6,8,10}. Suppose R is a 3-ary relation that is…

A: To determine the triples in the array.

Q: e) Suppose that S is an equivalence relation on a set A = {1,2,3, 4, 5, 6, 7}. If 4 e [3] n [5],…

A:

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: Let A # 0 be a set. Prove that A? is an equivalence relation on A.

A:

Q: Is the relation aRb → ab < 0 an equivalence relation on the set Z? Justify your answer.

A: Given a relation, aRb⇔ab≤0. To check whether R is an equivalence relation on set ℤ. A relation is an…

Q: State the formal definitions that a relation must satisfy in order to count as Reflexive, Symmetric,…

A: Reflexive relation: A relation R is reflexive over element X if every element X is related to…

Q: 9.42. Prove or disprove: The union of two equivalence relations a nonempty set is an equivalence…

A: We are asked to prove or disprove, the union of two equivalence relation on a non empty set is an…

Q: 3. Suppose that we have the following four tuples in a relation S with three attributes ABC:…

A: Given: Let us consider the four tuples, ABC:1,2,3,4,2,3,5,3,3,5,3,4. Let's determine the…

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: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5} If the relation is…

A: To find: (i)the given relation is equivalence or not.             (ii) The equivalence class.

Q: Let A = {cat, dog, bird, rat} and R be a relation on A defined by {(r, y) : x and y have at least…

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: Consider the following two statements: (1) If a relation on a nonempty set is reflexive, then it is…

A:

Q: 9.16. Let A = {a, b, c, d}. How many relations defined on A are reflexive, symmetric and transitive…

A: given A=a,b,c,d claim- how many realations defined on A are reflexive , symmetric and transitive and…

Q: If R = {(1,2),(2,1),(2,2),(3,4)} is a relation on the set {1,2,3,4}.The reflexive closure of R is :

A: Given that R=1,2,2,1,2,2,3,4 is a relation on a set 1,2,3,4  Consider A=1,2,3,4

Q: 9.12. Let S = {a, b, c}. Then R = {(a, a), (a, b) , (a, c)} is a relation on S. Which of the…

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.