6. A relation R on a set X is called a total order if it is antisymmetric, reflexive, transi- tive, and if all elements of X are comparable (that is, for every pair x₁, x2 € X either x₁ Rx2 or x2 Rx1). (a) Construct a total order on the set X = {a, B, Ⓒ, 13}. (b) How many possible total orders are there on a finite set of cardinality n?

Q: You just bought a new car from a dealership that sells cars no older than 2015. Consider the…

A: According to the given information, Let S be the set of all cars sold in the period 2015 to 2020.…

Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…

A:

Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

A:

Q: a)Let R be a relation on the set Z × Z defined by the following rule: For all (a, b),(c, d) ∈ Z × Z,…

A:

Q: In each item below, verify that ~ is an equivalence relation on the given set. Let S = Z × N. Define…

A: Since you have asked multiple questions, we will solve the Question Q (a) and (b) for you. If…

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: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

A:

Q: 3. Which of the following is an equivalence relation? Explain. (a) lives in the same city as (b) is…

A: Due to Bartleby answering guidelines I have solved only question no 3. Because you didn't mention…

Q: Q4) Let S be the set of registration numbers of students enrolled in a BSCS program in a university…

A:

Q: • Relation "z + y is divisible by 5" on integers z, y is an equivalence relation. Circle the answer:…

A: A relation R is called an equivalence relation if : R is Reflexive, i.e. aRa  R is Symmetric, i.e.,…

Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

A:

Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

A: The lexicographic ordering relation R on ℤ×ℤ is defined by, a, bRc, d if a>c or a=c and b≥d Show…

Q: Let A be a set and R and S be relations on A. Define the relation R+S on A by R+S = (R – S)U(S – R).…

A: Given A be a set and R and S be relations on A. R+S on A is defined by R+S=R-S∪S-R=R∪S-R∩S=R∪S∩R∩Sc…

Q: 9. Define a relation R on {-2,-1,0, 1, 2, 3, 4, 5, 6, 7} by a R b if and only if 3a+b is a multiple…

A:

Q: Consider the relation A ≤ B if the properties of A are also contained in the properties of B. Let S…

A: Partial ordering :                     A relation R on a set A is called a partial order relation if…

Q: set {(a,b),(a, a), (c, a), (b, b)} (a). Let X = {a,b,c} be sets. is a relation on X and find its…

A: Answer and explanation is given below..

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: 3. Let S = {1, 2, 3, ...}. Let R be a relation on he set S x S defined by (a, b) R (c,d) ⇒…

A:

Q: Let R be a relation from A to B and defined "x is at least twice as big as y." Write R as a set of…

A:

Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

A:

Q: 1. Let R be a relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by R = {(a, b) ∈ A × A | 4…

A:

Q: An ordering on a set F is a relation, represented by ≤, with the following three properties:(o1) For…

A: As per the question we are given a relation on a set F represented by ≤, with the following three…

Q: 4. For each relation R below, determine whether it is an equivalence relation on the given set A.…

A: Definition (Equivalence relation): A relation R is said to be an equivalence relation on a set A if…

Q: 1. Suppose A = {1,2, 3, 4} and the relation R on A is R = {(1,1), (2, 2), (3,3), (3, 4), (4, 4)} (a)…

A:

Q: 2. (p.214, #6) There are five different equivalence relations on the set A {a,b,c}. Describe them…

A:

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…

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: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. the equivalence…

A: The objective of the question is to understand how the equivalence classes for the given equivalence…

Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: For each relation R below, determine whether it is an equivalence relation on the given set A. Also,…

A:

Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…

A:

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

A:

Q: 1. Let A = {2, 3, 4, 5, 6} and B = {10, 11, 12, 13). Define a relation R on (A x B) as follows: a Rb…

A:

Q: f d a h с 6.0 g e b

A:

Q: Which relations are partial order? O None of the propsed relations O A={5,6,8,10,20} and R={ (a,b) e…

A: