In 1-8 a number of relations are defined on the set A = {0, 1, 2, 3}. For each relation: a. Draw the directed graph. b. Determine whether the relation is reflexive. c. Determine whether the relation is symmetric. d. Determine whether the relation is transitive. Give a counterexample in each case in which the relation does not satisfy one of the properties. 1. R = {(0, 0), (0, 1), (0, 3), (1, 1), (1, 0), (2, 3), (3, 3)} %3D 2. R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)}

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. Given a relation R on a set A, prove that if R is transitive, then so is R-

A: Transitive means aRb and bRc then aRc

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

A:

Q: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

A:

Q: Let A = {1, 2, 3}. Then show that the number of relations containing (1, 2)and (2, 3) which are…

A: The smallest reflexive relation on set A containing (1, 2) and (2, 3) is

Q: Prove that for any set relation R (we did not pick it to be "on" any particular set) R* =N{Q:RC Q^ Q…

A: Given that any set relation R.

Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

A:

Q: Given a natural number c ∈ N. On natural numbers, the relation Rc is defined as follows: ∀ a, b ∈ N…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

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: 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: 1. Consider the set Z in which the relation R is defined by aRb if and only if a + 3b is divisible…

A: According to question given that Set Z in which the relation R is defined by aRbIf and only if a+3b…

Q: Find, for each part of the question, an example of a set S and two relations R1 C S x S and R2 C S x…

A: Since the questions contains many subparts. As per the guidelines I am answering the first three…

Q: Draw the directed graph of the relation R on A = {1,2,3,4,5,6,7,8} defined as R = {(a,b)|a,b e A and…

A: Here, the relation is: R=(a,b)|a,b∈A and a≡b mod 3 That is: a-b is divisible by 3. So, 7-1=6 is…

Q: (a) We have defined the relations =6 and =10 to be certain subsets of Z². Their intersection R=…

A:

Q: Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b} is an…

A: Given, the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b}.

Q: Given a natural number c ∈ N. The relation Rc is defined as follows: ∀ a, b ∈ N :  (a, b) ∈ Rc ⇔ (∃…

A: According to Bartleby guidelines , i can give answer only first three subparts of your problem. I…

Q: Define the relation on the set Z of integers by if and only if a ~b if and only if a = b + 5k for…

A:

Q: that P ◦ Q is an equivalence relation on X iff P ◦ Q = Q ◦ P

A: Concept:

Q: 11. Prove or disprove: if a relation R is transitive, then R-1 is transitive.

A:

Q: 1. Let F be a nonempty family of transitive relations. Prove that NF is a transitive relation. Hint.…

A: Given that the F be a nonempty family of transitive relations.

Q: Let A = {6, 8, 13, 15, 9, 16} and define a relation R on A as follows: xRy ⟺ 7 |(x – y) Draw a…

A:

Q: Consider a relation ~ on the set Z such that x~y if and only if x + y is even. The relation ~ is…

A:

Q: 1. Determine whether or not the relation R on the set of all people is reflexive, symmetric,…

A:

Q: Given the relation R= {(1,1), (2.2), (3.3)(4.4), (1.2). (2.1) (3.4). (4.3)) on the set X- (1,2.3.4).…

A:

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: Given the relation R- {(1,1), (2.2). (3,3).(4.4), (1,2). (2,1). (3,4), (4,3)) on the set X…

A:

Q: 1. Consider the relation R on the set A = {0,1, 2, 3, 4}, defined by: %3D aRb + a = bc and b= ad,…

A: The given set is A=0,1,2,3,4 and the relation is defined as aRb⇔a=bc and b=ad (a) Check whether R an…

Q: 3. Given a relation R on a set A, prove that if R is transitive, then so is R-1.

A: We are given  that R is a transitive relation on a set A  Transitive Relation  A relation on a set X…

Q: Show that each of the following relations equivalence classes. on Z is an equivalence relation, and…

A: In the given question we have to find the equivalence classes.

Q: 1. Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: solution

Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

Q: Given a natural number c ∈ N. On natural numbers, the relation Rc is defined as follows: ∀ a, b ∈ N…

A: (a) let (a,a) be in Rc .      Then there exist integers u and v such that       au + av = c…

Q: 1. Let A & 2, 3, 4, 5, 6, 7, 83 and 9 and R a relation over A. Draw a directed graph of R after…

A:

Q: Let T be the relation defined by, For all a, b e Z, aTb iff a – b is odd. Is T an equivalence…

A:

Q: Suppose that P is a unary relation symbol, Q is a binary relation symbol, f is a unary function…

A: Note: According to bartleby we have to answer only first three subparts please upload the question…

Q: 5. For each of the following relations, indicate whether the relation is reflexive, anti-reflexive,…

A:

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: For the set A = {are, bot, cab, era)}, define the relation R on A to be: (x,y) eR if and only if…

A: As per the condition, in every order pair there should be only 1 letter in common.

Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

A:

Q: In problems 4, 5: show that the relation described is (1) reflexive, (2) symmetric, (3) transitive;…

A: Since you have asked multiple sub-questions, we will solve the first 3 sub-questions for you. If you…

Q: In 1-8, a number of relations are defined on the set A = {0, 1, 2, 3}. For each relation: a. Draw…

A: Given: The relation defined on the set A=0,1,2,3 is R2=0,0,0,1,1,1,1,2,2,2,2,3 We want to determine…

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: For each of the following, determine which of these choices is correct. Let Ry and Ry be two…

A: We have to determine which are correct.

Q: 1) Either prove or disprove the following statements: i) transitive. If binary relations T and S are…

A: Given: T and S are transitive  Suppose a,b∈T∩S, b,c∈T∩S ⇒a,b∈T, b,c∈T Now as T is transitive . So,…

Q: For (a, b),(c,d) EN×N define the relation (a, b) ~ (b,c) if and only if ab = cd. Is this relation…

A: Explanation of the answer is as follows

Q: Show that the relation R defined on the set of integers ℤ by (a,b) ∈ R if a – b = 6k for some k ∈ ℤ…

A:

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

A:

Q: 1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x²…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.