Let V, = xER for each positive integer i. Find each of the following. (Enter your answers using interval notation.) (a) 4 UV, = i = 1 (b) 4 i = 1 (c) Are V, V2, V3... mutually disjoint? Why or why not? O Yes, because no two of the sets V,, V2, V31 ... have any elements in common. O Yes, ecause the union of the sets V,, V2, V3, ... is empty. O Yes, because the intersection of the sets V,, V2, V3 ... is empty. O No, because no two of the sets V,, V2, V31 ... are disjoint. O No, because the sets V,, V2, V3r ... are disjoint. (d) n UV, = i = 1 (e) n i = 1 (f) UV, = 00 i= 1 (g) i = 1

Q: b. Prove that coth² x-1=csch?x

A: Sinh(x)= (e^x-e^-x)/2. Cosh(x)=(e^x+e^-x)/2

Q: 4. Let IR be the set of all real numbers, xER and n EN such that n 2 2. If (1+x)> 0, prove that Pn :…

A: Let ℝ be the set of all real numbers,  Let x∈ℝ and n∈ℕ such that n≥2 where ℕ is the set of natural…

Q: 2. Decide whether each of the following sets are finite, denumerable or uncountable. Explain each of…

A:

Q: What statement could be used to prove that m f n?

A:

Q: Determine the interval(s) on which x2 + 2x – 3 > 0. - Ох1 Ox 1 -3 1

A:

Q: For each of the following sets A, B prove or disprove whether AC B and BC A a) A = {r € Z: Byezt =…

A:

Q: Let V; = for each positive integer i. Find each of the following. (Enter your answers using interval…

A:

Q: 1] Find the supremums of the following sets by proving your results: a) S = {a < x < b; x E R}. b)…

A:

Q: 1 Find the absolute maxima and minuma x²-2x4+ bunded by y= x², y=t, the closed negion on %3D…

A: Given that, f(x,y)=x2-2xy+y Take the derivative for x, fx=2x-2y Take the derivative for y, fy=-2x+1…

Q: 2. Let a € R and n € Z0. Show that of the numbers a, 2a, distance from an integer is at most 1/n.…

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

Q: Find the supremum and infimum of the set x € R:x = +(-1)" ,n e N} + (-1)" ,n e N}

A:

Q: Find the supremum and infimum of each of the following sets. (a) A = {1, }. } ...} = {zin€N} 1 1 1 2…

A:

Q: S. Use the theorems and given information to show that r

A: The figure is as shown below : Given, ∠4 = (13x-4)o, ∠8 = (9x+16)o and x=5

Q: In general, if f(x) is real and continuous in the interval from x to xy and f(x1) and f(xu). between…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Let M = R and set Question 2 4= [(-1,5) N*]U ((8,9] (7,10]), B = {æ € R: \r-4|< A= 5x 15-51215} - 4…

A:

Q: If x and y are elements of an ordered integral domain D,prove the following inequalities:   x2- 2xy…

A: x2-2xy+y2=x2-xy-xy+y2=xx-y-yx-y=x-yx-y=x-y2

Q: For each of the following sets, find the maximum, minimum, supremum, and infimum IF THEY EXIST. S =…

A: When a set is bounded above, it has upper bounds. The least of all upper bounds is the supremum.…

Q: In the diagram, eleven circles of four different sizes are drawn. Each circle labelled W has radius…

A: Given problem is : In the diagram, eleven circles of four differentsizes are drawn. Each circle…

Q: Let X ~ N(0, 1). For any € > 0, show that P(|X| > c) ≤ ²c - ??

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Determine a and b such thatp(x) = x2 +ax+ bsatisfies p(l) = 0 and p' (1) = 4.

A:

Q: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A: topic - functions

Q: 4. Let R be the set of all real numbers, xER and n EN such that n 2 2. If (1+x) > 0, prove that Pn:…

A: Let ℝ be the set of real numbers, x∈ℝ and n∈ℕ such that n≥2. If 1+x&gt;0, we want to prove that  Pn…

Q: For every pair of integers x and y, if x – y is odd, then x is odd or y is odd.

A: Let x-is even integer and y-is even integer. x=2m, y=2n

Q: If Do, D1,..., Dn... nEN, are dense open sets of reals, then the intersection D = 0 Dn is dense in…

A: Condition: Dn is the open dense sets of reals, for all n∈ℕ. To find: Intersection of infinite open…

Q: Show that the intervals S [1,3] and T =[2,8] are equinumerous by finding a. bijection between them.

A:

Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

A:

Q: Find all the values of x in the interval [0,2pi], that satisfy the question.  10cos(x)+5sin(2x)=0

A: Given equation is Solve the given equation for x

Q: nd the supremum and infimum of the set D defined by D:= :neN

A:

Q: For each of the values on n and d given, find integers q and r such that n = dq + r and 0 is less…

A:

Q: Define sets A and B as: : {n E Z\n = 4r + 3 for some integer r}. • B= {m E Z m = 4s – 1 for some…

A: the objective is to solve the above questions.

Q: Define Floor: R → Z by the formula Floor(x) = for all real numbers x. Here are some example values:…

A: See the proof and counter example below.

Q: Which of the following is the interval containing the root if xi = 0.0000 and delta x = 0.1000. O…

A: we use the direct substituting the values of interval to determine the solution is exist or not in…

Q: The functions h and m are defined on the set R of real numbers by h:x→ ax +b and m:x → cx -d, where…

A:

Q: 9:Find the absolute exlemum Verlues of flx) x²-4x+24 over the interNal Cl,41

A:

Q: Let B, = {xER|0< x si for each integer i = 1, 2, 3, 4. (a) Find B, U B, U B3 U B4: (Enter your…

A:

Q: 4. Demonstrate that for positive integers t and Q, (t <= [V@]) is equivalent to (t x t <= Q). Show…

A: Given that t and Q are two positive integers and t≤Q To show that t×t≤Q Since from the given…

Q: 4. Show that the intervals S =[1,3] and T =[2,8] are equinumerous by finding a bijection between…

A:

Q: Consider the following relations, I-IV: Which of the following statements is correct? * I. R1(a,…

A:

Q: Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.

A: By adding the cubes of positive integers we solve the given problem.

Q: Let A = 3 21 then A-1 Does not exist O None of these equal to the above Dequal to the above

A: If determinent of metrix is zero then then matrix has no inverse

Q: Let, a1 = 3 and for n > 2, an = 2an-1 +1, express an in terms of n. %3D

A: We will find out the required expression in the term of n.

Q: Find the value of k such that A is singular. (Enter your answers as a comma-separated list.) 0 k 1 k…

A: We have to solve the matrix

Q: Suppose A and B are bounded and nonempty subsets of real numbers and 1 E R. In this case: sup(AB) =…

A: Suppose A and B are bounded and nonempty subsets of real numbers and λ∈R. We need to prove that…

Q: (c) If A E M,(R) is non singular and n 2 2, prove that det(adjA) = (det A)"- (d) If A E M,(R)…

A:

Q: Select each step to complete a proof by contrapositive of the theorem below. Theorem: For every pair…

A: Here we have to prove the theorem that “For every pair of integers x and y, if 5xy + 8 is even, then…

Q: For which positive numbers a is it true that a" > 1 + x for all x?

A:

Q: Q3. Let z, y be real numbers such that ry 1 and z #y. Prove that

A:

Q: "for all n,m ∈Z \ {0} and g ∈ N,  gcd (n,m)= g then there are a,b ∈ Z with an+bm= g" is the…

A: We need to see if the converse of the statement "gcdn,m=g then there are a,b∈Z with an+bm=g" is true…

Q: Given 8 - 4cos'x + 8sinx = 9, find x for the interval 0 s x < 360° O 45°, 135° O 60°, 120° none of…

A: