4.4.6 Determine if the following relations are reflexive, irreflexive o ther (a) The relation x < y on the set Z. (b) The relation "x is married to y" with domain and codomain the a of all people in the USA (c) The relation r= { (x, y) e N x N: x-y = 1 }. Scanned with CS CamSca (d)eThe relation r2 = {(3, 4), (4,4), (2, 3), (3, 3), (1,2), (2,1), (4,3).

Q: 9.J. If F is a non-empty closed set in R and if x ¢ F, is there a unique point of F that is nearest…

A: As per BARTLEBY GUIDELINES, I answered one question (Q-9.J.) and repost other questions separately.…

Q: 2 Let F be a closed set for k = 1, 2, ... , n in (S, d). Show that |J F, is closed. k=1

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 0,1,2

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Q: 7.1.4 A relation is defined on N by a Rb + ; E N. Let c,d E N. Under what conditions is it…

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Q: Let X = {x E Z+ | 15 < 4x < 22} and Y = {y is even | 0 < 2y +1 < 15}. Define a relation R from X to…

A: We have to find the elements of X and we have to define a relation R from X to Y.

Q: 8. Which of the following theorems can be applied on f(x) |x| on the interval [-1,1] a) Rolle's…

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Q: Consider the graph of f. 5 1 + 1 2 3 4 5 6 7 8. 9. Determine the correct statement(s) about f'(x). O…

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Q: 2. Let a, b e R and let f be the function Z + Z defined by f(z) - ar + b. For which values of a and…

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Q: Prove this is an equivalece relation. x related to y iff x2 -  y2 is even

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Q: 10.9. Determine which of the following five relations R; (i = 1, 2, ..., 5) are functions. d. R4 is…

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Q: Let Y = {0,1,2} and Z = {0,1} and define a relation R from Z to Y as follows: Given {x, y} € Z x Y,…

A: Relation : A relation between two sets is a collection of ordered pairs containing one object from…

Q: C. Let T be defined onN N by (a, b)T (c, d) if and only if a c and b 2 d. Write down the full nature…

A: We will use the basic definition of reflexive, symmetric, antisymmetric and transitive realtion.

Q: 8. For each of the following relations on N, determine which of the properties are satisfied. (a) S1…

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Q: 1. Let Y = (0, 1, 2) and Z = (0, 1) and define as relation R from A to B as follows: Given any (x,…

A: (NOTE- The relation R should be from Y to Z instead of A to B.) Given sets are, Y=0,1,2 and Z=0,1…

Q: 4. Consider the following relations R on the integers Z. For each of these relations, say whether…

A: For the solution of the problem follow the next steps.

Q: (a) Show that the formula (VæR(g(x), x) = Vx3yR(y,x)) is universally valid, where g is a 1-place…

A: Part(a): As we know, ∀xRgx,x⇒∀x∃yRy,x Where g is a two place function symbol and R is a two place…

Q: 1 LetXbeadiscreterandom variablewithprobabilityfunctionp(x), g1(X),g2(X),g3(X),···,gk(X) be k…

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Q: 16.1. Give an example of a bounded and continuous function g on R to R which does not take on either…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 1. For the following, each relation R is defined on the set A. Determine if R is a tree, if it is,…

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Q: Now let G = S_10, acting on the set {1,2,3,4,5,6,7,8,9,10}. What is the index in G of the stabilizer…

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Q: 11. Find the domain of the following function. Write the domain in interval notation. oniylggs bns…

A: We have to find the domain of the function h(x) = 1/√(x2-2x-8)   x2 - 2x - 8 = 0 x2 - 4x + 2x - 8 =…

Q: Given the relation of this table: 1|0 S 1|0|3 2 What is the rule for this relation? O 3 (n +1) 6 O 2…

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Q: 4. Given s and t, relations on Z, s = {(1,n) : n € Z} and t = {{n,1) : n E Z}, what are st and ts?…

A: Solution

Q: 1. We'll need to establish the Schröder-Bernstein Theorem first. Assume there exists a 1 – 1…

A: Please see below picture for detailed solution.

Q: 10.18. Let A = {w, x, y, z} and B= {r, s,t}.Give an example of a function f: A →B that is neither…

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Q: 10.9. Determine which of the following five relations R; ( i =1,2,..., 5) are functions. a. R1 is…

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Q: 8. Give an example of two relations S and T such that R = the domain of S = the domain of T= the…

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Q: Q1 Given a relation R on Z defined by mRn7|(mn) for all m, n € Z. Find the equivalent class…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Does the follorin relations hip define y as a real furction of x Why," AN

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Q: Draw Ogives” less than” and “more than “on the same graph paper for the following data Class…

A: An ogive is drawn by the help of cumulative frequencies. It plots the less than and greater than…

Q: (c) Suppose n = 5 and m = 4, determine the number of onto functions from A to B.

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Q: 6. Is the function h: Z → Z defined by ( 2n if n 20 h(n) -n if n < 0 one-to-one? Is it onto?

A: The solution is given as follows

Q: Let G = { -2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows: For all (x, y)…

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Q: 4. Let G = {–2, 0, 2} and H = {4,6, 8} and define a relation V from G to H as follows: For all (x,…

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Q: 4. Let n e N with n > 1, V = Z and set E = {{r,y} : x, y E Z and |x – y| = n}. Define G„ = (V, E).…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 1 Recall that for x, y ≤ R, |x − y| ≤ Rf is the absolute value of x - y. That is, if x-y≥0 |x - y =…

A: Please see the below picture for detailed solution.

Q: LetXbeadiscreterandom variablewithprobabilityfunctionp(x), g1(X),g2(X),g3(X),···,gk(X) be k…

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Q: 14 13 12 11 10 17. -5 -4 -3 -2 Which of the following functions is shown on the graph o fle) = () 4…

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Q: {d, e, f, g}. Define 8. Let X = {a, b, c} and Y = functions H and K by the arrow diagrams belov…

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Q: Let fi = 1+x + æ?, f2 = 3+ 2x + a?, fs = 1+ 2x + 3x?, fa = 1+ 3x + 5æ?. 1 -1 is a dependence…

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Q: 7. Define a relation M from R to R as follows: For all real numbers x and y, (x, y) e M means that y…

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Q: Let Y = {0,1,2} and Z = {0,1} and define a relation R from Z to Y as follows: Given {x, y} € Z × Y,…

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Q: 6 Suppose that a function h satisfies –x² < h(x) < x² for all x. Prove that h is differen- tiable at…

A: Definition used: f'x=limh→0fx+h-fxh and f'a=limh→0fa+h-fah Calculation: Consider the given…

Q: 3. Eliminate B and a from the relation x = Bcos(wt + a) in which w is a parameter not to be…

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Q: Let X = {x € Z+ | 15 < 4x < 22} and Y = {y is even | 0 < 2y +1< 15}. Define a relation R from X to Y…

A: ANSWER ONLY ASAP! What are the elements of the Cartesian product X x Y?

Q: Let S = {(x,y) : x, y € R} = R². Define an equivalence relation on S (i.e. a subset of S × S = R² ×…

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Q: If z(m) denotes the factorial function of order n then show that A"z(m) = n!h" where h is difference…

A: Use the definitions of forward difference operator ∆fx=fx+h-fx and the  nth factorial of x, to find…

Q: a L4 D 2 of 5 disprove that R is a partial order : {(a,b) : 3keza = k * b} be a relation over the…

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Q: 14,497 where y is the 55000 and older with at least a indicates a linear relation nt of 0.7581.…

A: Note:As per the requirement of the students solving part(c). Let Y= a+bX be the regression line.…