4. Let S = {1, 2,..., 10}. Out of all the equivalence relations on S that have exactly 2 equivalence classes, an equivalence relation is chosen uniformly at random. What is the probability that it has two equivalence classes of size 5?

Q: c) For a set X = {1,2,3, 4, 5}, let P be the partition {{1,3, 4}, {2}, {5}}. In the equivalence…

A: Q1(c) asked and answered.

Q: 1. Determine whether each of the following relations on the set {1, 2, 3, 4} is reflexive,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1. Let H = {1, 2, 3, 4, 5} and the rlation RC H², with (a, b) ER + a = b( mod 3). • Give the set R.…

A: R ={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}

Q: Every equivalence relation is reflexive. True False

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

Q: Let A = {a,b, c, d, e, ƒ}, and let G and H be the following equivalence relations in A: G = IA U…

A:

Q: 8. Draw the directed graph of the binary relation S on B = { a, b, c, d, e} by S = {(a, b),(b,…

A:

Q: 5. Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - UB, = N(A – B,).…

A:

Q: How many equivalence relations on A=|42| are there that have distinct equivalence classes of size 4,…

A: Given A=|42| and distinct equivalence classes of sizes 4, 7,7, 8,8, and 8.

Q: 1. Find all equivalence relations on{1,2,3}.

A: Given set is, 1,2,3

Q: Need help trying to solve this

A:

Q: A set of dice is called intransitive (or non-transitive) if it contains three dice, A, B, C, with…

A: There are three dice, which have the following faces: Die A= {2,2,4,4,9,9} Die B= {1,1,6,6,8,8} Die…

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: 24) 100 people are surveyed, obtaining the following information: -Every respondent who owns a car…

A: Given that the total number of respondents is 100. There are 54 male respondents. The number of male…

Q: 3. Let S be the congruent modulo 2 relation on Z, that is m S n 2|(m-n). Show the relation

A:

Q: 7. Let R be the following equivalence relation on the set A = {1,2,3,4,5,6};: R = {(1,1),(1,5),…

A: Equivalence class of R= R  =a=x∈A :aRx 1=1,52=2,3,63=2,3,64=45=1,56=2,3,6

Q: Let R = { (1,1), (3,1), (2,1),(2,2), (1,3) } be a relation on the set A = {1,2,3}. Construct a…

A: The set A×A={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} R={(1,1), (3,1), (2,1),…

Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: 4. Suppose Rand S are symmetric relations on a set A. Prove that RoS is symmetric iff Ro S = So R.…

A: Suppose R∘S is symmetric Let s, r∈S∘R ⇔r, s∈R∘S⇔s, r∈R∘S ( since R∘S is symmetric)  So, R∘S=S∘R

Q: Let S = {0, 1, 2, 4, 6}. Test the following binary relation on S for reflexivity, symmetry,…

A:

Q: The participation of relation R can be: total, partial, onto, and into. Given A = {1, 2, 3, 5} and B…

A:

Q: 2. Determine the partition of B = {1,2,3,4,5,6,7,8,9,10} induced by the equivalence relation B…

A:

Q: 3. Let S be the congruent modulo 2 relation on Z, that is m S n→2|(m-n). Show the relation S is: (a)…

A:

Q: 11 Let S be the congruent modulo 5 relation on Z , that is m S n → 5|(m – n) . Show the relation S…

A:

Q: Define the relation∼ on Nby m ∼ n if and only if the sum of the distinct primes that divide m is the…

A: To test if the given relation satisfies the conditions for reflexivity, symmetry and transitivity

Q: 5. Let A = {41, 49, 67, 71, 73, 76, 81, 88, 111} and R be an equivalence relation defined on A where…

A:

Q: 1 A class of 40 students was each required having three textbooks in each of Economics, Mathematics.…

A: Topic:- ven diagram

Q: 6. Consider the partition P = {{0}, {-1,1}, {-2,2}, {-3,3},{-4,4},...} of Z. Describe the…

A: Given the partition of Z is P=0,-1,1,-2,2,-3,3,-4,4,....

Q: If {{1, 3, 5}, {2, 4}} is a partition of the set A = {1, 2, 3, 4, 5}, determine the corresponding…

A:

Q: Let A = {1,2,3,4,5} B= (6,7,8,9} Define an equivalence relation of p in A UB with atleast 12 members

A: A=1,2,3,4,5B=6,7,8,9A∪B=1,2,3,4,5,6,7,8,9

Q: 2.3) Suppose A, C A2 C …· are o -algebras consisting of subsets of a set X. Is U, A¡ necessarily a o…

A:

Q: 1. Show that R is an equivalence relation on P(A). 2. Set A = {1, 2, 3, 4} and B = {1, 24}.…

A:

Q: (Chapter 11.4, #3) The relation relation. Sketch it, by drawing Z as a subset of the line, then…

A: The objective is to show that x≡ymod4 is an equivalence relation. To show the relation is an…

Q: 6. Find all equivalence relations on {1,2,3}. 7. Show that for n, m ɛ Z+, gcd(2" – 1,2m – 1) =…

A: Note : We are entitled to solve only one question at a time and up to 3 subparts only. To find -…

Q: 3. Let S be the congruent modulo 2 relation on Z,that is m S n→ 2|(m-n) . Show the relation

A: A relation is called symmetric if for any  if  then we have .

Q: 3) Let S be the equivalence relation on P({0, 1, 2, 3}) defined by XSY if and only if ged(X], 4) =…

A:

Q: How many equivalence relations on the set {1, 2, 3}? 1. О З 2. O 6 3. О 5 4. O 4

A: The objective is to find the total equivalence relation on set {1,2,3}.

Q: Let S = {0, 1, 2, 4, 6}. Test the following relation whether it has equivalence relation on S. R =…

A: Given relation R = {(0, 0), (1, 1), (2, 2), (4, 4), (6, 6), (0, 1), (0, 2), (1, 2), (4, 6)} on  S =…

Q: Which of the following are equivalence relations? If they are not, which of the axioms fails? a) For…

A:

Q: 5. Let X and Y be sets and let f: X→Y be onto. For all be Y, let As = f-¹({b}). (a) Prove that P =…

A: Given that X and Y are the sets , f : X→Y be onto function and ∀b∈Y, Ab=f-1b. To prove: (a) P is a…

Q: Let R be the set of all binary relations on the set {1, 2, 3}. Suppose a relation is chosen from R…

A: Introduction :Given , R : set of all binary relations on the set {1,2,3}We have asked to find the…

Q: . Let S = P({1,2,3,4,5}.. Define equivalence class of the set {1,2,3}. equivalence relation ~ by X~Y…

A: Consider the given information:

Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…

A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~  is defined by,        "x1,x2~x3,x4 only if…

Q: e. If x is a subset of V of cardinality 2, then f (x) is the edge connecting the two vertices in x.

A:

Q: Let A1,A2,.......,An be countable sets. Prove that  A1 x A2 x.............An = { a1, a2,…

A: Let A1,A2,.......,An be countable sets. Then we have to show that    A1 x A2 x.............An = {…

Q: Let I be the set of equivalence classes as defined as above. Define O as follows: if A and B are…

A: The multiplication for: Take, . Then,

Q: Let R be the divisibility relation (|) on A = {3,5, 6,7, 10, 20, 30}. We know that (A, |) is a…

A:

Q: (10) Every finite closed communicating class is recurrent. FO

A: Given problem Given that   Every finite closed communicating class is recurrent. T It is True Option…

Q: Which of the following relations is the a partial ordering on the set A = {3,7,9}? O…

A: A relation R on a set A is called a partial order relation if it satisfies the following three…