2. Write a preference E on R as a subset of R', where a bundle a E Rª is at least as good as a bundle y E R if the larger coordinate of x is greater than or equal to the larger coordinate of y. Is this preference rational? Does it have a utility representation?

Q: Discrete math.  Let S = R. On S we define the relation R as follows (∀x)(∀y)(xRy ⇔ y ≥ x + 3). Is R…

A: The given set S=ℝ. The relation R defined in the set S is ∀x∀yxRy⇔y≥x+3. We have to check whether…

Q: ercise 6.67. Let E be a subset of R having at least two points. Pro- owing are equivalent:

A:

Q: 4. Consider the following binary relation p on the plane R² (x, y)p(u, v) if y? – a² = v² – u².…

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Q: 2. Let x be an element of a convex set S. Assume that x1 = x + €ip E S and x2 = x – €2P E S, where p…

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Q: II. Show that if preferences 2° € X*. strictly convex, then A'(xº) is strictly convex for each are

A: Use the preference criteria to prove the following. Show that in each case, they are convex.

Q: 2. 1. 5. 2. up 2. Example, :find the produck ר

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Q: 10.4. For the given subset A; of R and the relation R; (1<i< 3) from A; to R, determine whether R;…

A: We have to determine whether Ri is a function from Ai to R or not .

Q: Evaluate e fry²dæ + x³dy, where C' is the rectangle with vertices (0,0), (4,0), (4,2), and (0,2)

A: We apply the green's theorem to solve the given problem.

Q: Graph these parametric equations on the TI and include screenshots x = 2t – 2 sin t, y = 2 – 2 cos t…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

Q: Exercise 2. Which of the following maps o : (a) $(r, y) = (x², r*, y) %3D

A: Please find the sol in next step, Shall we solve one question only as you have asked more than one…

Q: Given a relation from Z (positive integer) to Z (positive integer) is defined as follows: ((m, n) E…

A:

Q: 0 IS SU b) Let f be a map. from a space X ipto a space Y and 6 is a base for Y .show that f…

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Q: Evaluate Ja xdx + ydy + zdz where C is the line segment from (3, 4, 1) to (4, 5, — 1).

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Q: 6. Let R be the following relation on {a, b, c, d, e}. MR = (ants) Represent R with a digraph. TULLE…

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Q: 11. Define F:Z × Z→Z × Z as follows: For every ordered pair (a, b) of integers, F(a, b) = (2a+1, 3Ь…

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Q: 6. (a) Let A, B, be subsets of R. State the conditions which make the pair (A, B) Dedekind cut. (b)…

A: It is given that Let A, B be subsets of R.

Q: Define a relation on Z by aRb if and only if a divides b. Is R an equivalnce relation? Why or why…

A: To define a relation on the set of integers Z, denoted by "aRb," where "a" divides "b," we need to…

Q: (#4) Show that a set SCR" is closed if and only if bdry(S) CS.

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Q: ADDITIONAL EXERCISES: These exercises are NOT REQUIRED to be submitted. However, you can try these…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: c) Find the characteristic polynomial of each of the restricted maps Tw and Tu. d) Determine whether…

A: Given that,  V=ℝ4 and T be the linear operator on V defined by, Tx,y,z,t=3t, -y+4z, 5y, x-2t c) To…

Q: 1. Decide if the following statement is True or False: %3D Let A1, A2, ..., Ak E Mnxn(R) be such…

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Q: 5. Let A = {1, 2} and B x+y y) e R such that {3,4}and define a relation from A to B as (x,y) e AxB…

A: We will find out the required values.

Q: 4.4.4 List the relation on N defined bv h(x, y) e N x N : x > y } 9 Scanned with CS CamScanner as a…

A: The relation given is already a subset of the Cartesian product N x N. It can be written as follows.

Q: Let R be the relation on N defined by x Ry if x and y share a common factor other than 1. Determine…

A: xRy implies that If x and y share a common factor other than 1, then this implies that If y and x…

Q: Part II: Prove/Disprove the following 2. Let R be the relation on Z, defined as follows: Vm, n e Z,…

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Q: Arrange the choices in order 1,2,3.. to prove: For any sets A, B and C Ax (BUC) = (A x B) U (A x C),…

A: SOLUTION-

Q: Let R be an equilene relation defineed an IN as follows ! 2-8(x)ENIN Y-y alivisible by3}

A: It is given that let r be an equivalence relation defined an 1n as follows R={(x,y) belongs to N*1N…

Q: If geRla,b] and if h(w)= gcu) encept %D finite number f points for [a, b],'then and in of prove that…

A: First we have to divide the set into finite subsets of x intervals required.

Q: 3.7 Consider a fuzzy relation R CAXA where A = {a, b, c}. R a b e 1 1 1 1 1 1 d 1 1 1 a) Determine…

A: Solution :-

Q: etermine the equation of your model that will pass 2,4

A: We already have the equation of polynomialand

Q: 2. Let U = {a + bx + cx2 + d³ e P3 (R) | a- 6+d3D0}, and let W = {a + bx + ca? + dx³ e P3(R)| a + 2c…

A: