) The domain is a group of people. Person x is related to person y under relation S if x is currently the spouse of person y. You can assume that there is no polygamy and that there is at least one person who is married to another person in the group.   b.) The domain is the set of all integers. xEy if x + y is even. An integer z is even if z = 2k for some integer k.

Q: A relation Ron A is an equivalence relation if it is reflexive, symmetric, and transitive. Given: A…

A:

Q: Given a set define a relation induced by a partition of set A and that partition must consists of at…

A:

Q: 6. Let X = {1,2,3,4, ... ,16}. Define xRy to mean that 5 divides x - y. a) List the elements of R-1.…

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: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

Q: 2. State the domain and range of each rela d) c) 1 b) 8 8 4 8 4 4 -8 8 4 8 8- 4 O 8 4- 8- -4- lo ↑y…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Let A be the set of all citizens of New York City. For a, b E A, define a ~ -b if and only if ●…

A: To show that ~ defines an equivalence relation on the set A (the set of all citizens of New York…

Q: The set {{8}, {9, 10}, {11}} is a partition of the set A. Define the equivalence relation R on the…

A:

Q: 1. Let the set A = {1,2, 3, 4, 6, 8, 12, 24) be partially ordered by the relation ab. Illustrate the…

A: As per our guidelines we are supposed to answer only first one. Kindly repost other parts in the…

Q: 2. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose R has two equivalence…

A:

Q: Draw the Hasse Diagram for the set B = {1,2,4,5,10,15,20} where R is the "divides" relation. Mark…

A: Hasse Diagram:  Pictorial representation of partially order set is known as Hasse diagram  Least…

Q: 4. Let A = {a, b, c, d}. Suppose R is an equivalence relation on A. Suppose R has three equivalence…

A: To Determine: write R as a set .describe then all   Given: let A={a,b,c,d} suppose R is an…

Q: 2. For each equivalence relation below, find the requested equivalence class. a. R = { (1,1), (1,…

A: As per our company guidelines we can solve only the first three subparts. Kindly re Post the other…

Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

Q: Segment congruence theorem. Segment congruence is an equivalence relation. In other words, if PQ, RS…

A: If PQ≅RS then by definition, d(P,Q)=d(R,S)...(equation 1) and if RS≅UV then by definition,…

Q: For set S = {1, 2, 3, 4}, we define the following relations R1 = {(2,2), (2, 3), (2, 4), (3, 2), (3,…

A:

Q: Subject: Set Theory

A:

Q: roblem 0.2. Which of the following examples are equivalence relations? (1) S is the set of real…

A:

Q: Consider the set of all members belonging to the same family and the binary relation defined as " to…

A: GIVEN: The set of all members belonging to the same family and the binary relation defined as " to…

Q: Visualizing equivalence relations. Draw all of the equivalence relations on a set with three…

A:

Q: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

A: According to the given information it is required to check whether the given relation in each part…

Q: Let N be a nonempty set and o a permutation of N. Define a relation a~b if and only if b = o"(a) for…

A: Given, Ω is a nonempty set and σ a permutation of Ω. A relation on the set is defined as a~b if and…

Q: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

Q: Let P be the set of all people. Consider the relation pNq if p and q have the same first name. Which…

A: Given thatP be the set of all people.Consider the relation pNq if p and q have the same first…

Q: Diamond Property: Let R be a binary relation. We say that R has diamond property if, whenever aRb…

A:

Q: Let A, B, and C be sets. Prove or disprove: If R and S are equivalence relations on A, then S o R is…

A:

Q: Ris an equivalence relation on a set with 5 elements. Which of the following are possible? There are…

A: We know equivalence classes are disjoint classes. Since R has 5 elements . Hence , possible cases…

Q: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

A: a) Consider the given relation M. To prove M is an equivalence relation. For that, M must be…

Q: Let A = {a, b, c, d, e}. Suppose R is an equivalence relation on A. Suppose R has two equivalence…

A:

Q: Give at least three different examples of equivalence relations.   Note: In every example please…

A: A relation R on a set A is said to be an equivalence relation if and only if the relation R is…

Q: Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are,…

A: Given R and S are two Poset on a set X. (1) Consider R∩S. Since R and S are poset, therefore each…

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: Consider the set A = {2, 3, 5, 10, 14, 19, 21} and the relation Va, b A, a Rb a = b mod 8. List all…

A: