Let x, y ∈ R. Assume that x < (1 + z)y for all z ∈ R with z > 0. 1. Show that 0 ≤ y. 2. Show that x ≤ y.

Q: (c) For the set A = {[0], [6]} ≤ Z12 determine the set U = h(A). Then for the set UC Z18 determine…

A: In group theory, sets like Z12​ and Z18​ are examples of cyclic groups under addition modulo 12 and…

Q: EXvyP(x, y) is true when there is an x for which P(x, y) is true for every y. A True B False

A:

Q: Q. AfX-Y where X,Y € Z* , and 0<X <23 and, 0s Ys59, X is hour of clock and Y is minute of digital…

A: Given: f: X→Y , where X is hour of clock and Y is minute hand of clock It can be clearly observed…

Q: 1. Let h : R → R be some twice-differentiable function. Define f(x,y) =h() for all x ≠ 0. Show that…

A:

Q: Describe the following sets in terms of graphs, supergraphs, and subgraphs of functions appropriate:…

A: let's break down each set step by step.Set A: {(x, y, z) | y^2 + x &lt; yz ≤ x + y^2 + z^2}1. Graph…

Q: (a) Determine whether or not it is convex or concave. A = {(x, y) = R²|yx4, and -2≤ x ≤ 2} B = {(x,…

A: Necessary Sufficient Nature f'x0=0 f'x0=f''x0=f'''x0=..=fn-1x0=0  fnx0&gt;0 n even Convex f'x0=0…

Q: 4. Let R be the relation in the positive integers

A: 4. Given, R be the relation in the  positive integers ℕ defined by                        R=x, y: x,…

Q: 1. Find the absolute extreme points {x-cord., y-cord.), max the given interval, f(x)=x' - 3x² – 4…

A:

Q: Which of the following sets are equal? A = {0, 1, 2} B = {xE R| –1<x<3} C = {x E R|-1 <x< 3} D = {x€…

A: first we convert the given roster notation to set or interval notation then compare. ℝ=(-∞,…

Q: Which one of the following relations is not a function? O ((x.y): r, y ER and r + y² = 1) O ((x.y):…

A:

Q: Let W = (0, 1, 3}, X = {1, 3, 5), Y = (3, 4} and Z = {(1, 2), (3, 4), (1, 3),(2, 4). Compute (X x Y)…

A: The given problem is to find the Cartesian product of given sets and verify the Cartesian product…

Q: 5. Let (a, b] denote an interval of the real axis, containing the boundary Doint b, but not…

A: Answer given below.

Q: Let f(x, y) = x(y - 3) and F = Vf. If r = with 0 ≤ t ≤ 2, then [F. dr is equal to: a. -7 b. -11 c.…

A: We find the line integral in the following way

Q: 16. Let vo = (a, b) and let v = (x, y). Describe the sets of points in R? satisfying the following…

A: Given v0=a,b, v=x,y

Q: 5. Prove that if x, y ER, then x + y ≤ x + y. Use the following cases: (i.) x, y ≥ 0, (ii.) x, y <…

A: We now prove that if x,y ∈ ℝ , then x+ y≤ x+y with the help of given three cases.

Q: Find the of im < Re z< £ un der w-

A: Substitute w=u+iv and z=x+iy in the transformation. w=1zu+iv=1x+iyu+iv=x-iyx+iy.1x-iyu+iv=x-iyx2+y2…

Q: Let (X, CA) be a measurable space, f: X (-00, ws) and 1: X (-∞, ∞0) are measurable. Prove that the…

A:

Q: Prove both sides equal If T ≤p and π ≤v, then TUT ≤p Uv. τ υπ

A:

Q: 7.) If xy is negative, which of the following is possible? a. x < y < 0 b. x < 0 < y c. x = y d.…

A:

Q: 4.4. Let S be a nonempty set. Suppose that to each ordered pair (x, y) E S x S a nonnegative real…

A:

Q: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

Q: 2b. In R show that : || x - y || || x + y || ≤ 11x11 ² + 11y11²2² -(1

A:

Q: Prove. For any x, y ∈ R and x < y, ⟨(x, y), ≤⟩ is not well-ordered, where (x, y) is an open interval…

A: To Prove: x,y,≤ is not well ordered, where x,y is an open set with the usual order "≤".

Q: 7. ) Let f: N→ Z with f(n)=n+4. Let A = {1,2,3} and B = {1 € Z \ I <10). Use these to find the…

A:

Q: Let f(x, y) = x for y=0 and 0 for y+0. Evaluate each of the following or if they do not exist, state…

A:

Q: 1. Let S² = {(x, y)x² + y² = 1}. Define the operation of addition on this set by taking (x, y)+(u,…

A:

Q: Let x, y, z be positive real numbers such that x² + y² + z² = xyz. Prove th following inequalities:…

A:

Q: For each of the sets find the set of boundary points and the set of interior points. Also state if…

A: We have, (a) [0,1]U{4} (b) x,y∈ℝ2:x2+y2=1 Here we have to find the  o find: Interior Boundary…

Q: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

Q: Suppose X and Y are independent. Find Pr[X Compliment |Y ] if Pr[X ∩ Y ] = .42 and Pr[Y ] = .6.

A: According to the provided information,

Q: If X is uniform on [2, 6]. Find a. P(X > 3), b. P(4 ≤ x ≤ 5)

A: X~U(a,b) probability density function pdf of uniform distribution is.  f(x)=1/(b-a)  , a&lt;x&lt;b

Q: Prove by direct method: if x, y>0  such that x ≤ y then √x≤√y

A:

Q: b. SSR ехту dA_ where R = {(x,y) | − x ≤ y ≤X, 0±× 6 2}

A:

Q: Let A = {y ∈ Z : 2<y ≤ 14 and y is even}. What is |A|?

A:

Q: 2. Let a,, az,.., a, be numbers. Show that there is a single number r such that foxo: (-a,) + (z –…

A: Solving

Q: 2.4. Let J and J be real valued functions defined on a subset of a linear space Y, and suppose that…

A: We will use basic knowledge from the theory of calculus of variations to answer this question. You…

Q: For functions:f(x, y) = x − yg(x, y) = x2 + x − yDetermine whether the following sets are closed and…

A: Final answer:.a) Not bounded.b) Not bounded.c) Not bounded.d) Not bounded.Explanation:Explanation:…