Find   ∞ ∪ i=1 Ai       and       ∞ ∩ i=1 Ai                   i an integer To show your work, show the first three values of each (i.e., A1, A2, and A3). Ai = { i, i + 2, i + 4, . . . } Ai = { 1, i+1 } Ai = [ 2, i ], that is, the closed interval of real numbers x between and i, inclusive of the end points Ai = [ i+1, ∞ ), that is, the interval of real numbers x with x ≥ i+1 Ai = ( −∞, i ], that is, the interval of real numbers x with x ≤ i

Q: Prove that (-1ti3)" + (-1-is3)" has either the value 2n+' or the value -2" if r is any ). integer…

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Q: N.Find the set of values of x for which: w - x-2 x+1 12. Solve the inequality:(x-3)(x+2)(x+4) > C 13…

A: 11)  xx-2>1x+1⇒xx-2-1x+1>0⇒xx+1-x+2x-2x+1>0⇒x2-2x-2x+1>0           1 If x<-1 then…

Q: The domain of a quadratic function is (-o, x). O True O False

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Q: Let a = (-2,3, –4)" , y = (3,-2, -5)". (a) Find ||a||1. (b) Find ||a||2- (c) Find ||y||o-

A: Given Information -  x = -23-4  and  y = 3-2-5We have to find the following - (a) x1(b) x2(c) y∞…

Q: For the function f(x) = 5x° -4x +2x + 3, findf "(x). Then find f"(0) and f"(4). f"(x) = Select the…

A: Double derivative

Q: Which x satisfies both Ix - 31 < 2 and Ix - 51 < 1?

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Q: Find The Domain and Range * V2x-3 х2-5х+4 Df : [3/2, 0) / x-{4,1} , Rf : Real Number Df : [3/2,- 0 )…

A: Here we have to find the domain and range;  f(x)=2x-3x2-5x+4

Q: A0) = 2, A2) = 5 and f(n) = 2 An - 1) +3 (n - 2) + fAn - 3) for all n> 3. Find f(4).

A: Solution:

Q: 4. Select all the true statements about the end behavior of the function f(x) = -x*-5x .4 + 5x +3.…

A: Given :

Q: sing direct proof, prove the following statements: 1. Prove: If x2-4=0, then x = 2 or x = -2. 2. If…

A: follow next step

Q: Find A, B, AB, and [AB]. Then verify that |A||B| -2 1 1 ^-[¯² _²]- ® -[ 1 _²] A = 4 -2 -1 (a) |A|…

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Q: Use proof by contradiction to show that there is no positive real number x such that (x-2)/x ≥…

A: In an inequality, if a positive number is multiplied then there is no change of sign of inequality.…

Q: Prove that for all real numbers Ex)y= -(1u)

A: We have to prove that for all real numbers (- x)y= - (xy)

Q: Find all positive integers a, b such that a | b^2-b+1 and b | a^2-a+1

A: Solution :-

Q: Funchion figandx are follows f(2)- H-14 +421, g12)= Tio-22 , hca)- 5+x find, Find %3D 2. g (4) = h…

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Q: 16. Find the set of real values of x for which:/3 - 2x/S/x + 4/. N.Find the set of values of x for…

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Q: Let R be the set of real numbers, C= (0, 10], D= (9, 15], E = {1, 2, 3} and F= (7, 10). Find: (i)…

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Q: Describe the set of real numbers x for which x + 2/ x − 5 > 1

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Q: 4. Find a number 8 >0 such that if Ix-10] < & then |(2x + 3)-23|< 0.25.

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let A = B = C = {x 1 x is a real number}. Let f: A → B and g: B → C be defined as follows: f(a) 2a…

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Q: Domain:[-3,0) U (0, 1) U {3U (, ∞0) Range: [-6, -3) U (-3,-2) U{-1U (1, ∞)

A: simplify what it means after the third U in both answers . like write it in another way...

Q: If the domain consists of all real numbers, just type t = 00 with tw To input the symbol +, type !=…

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Q: Which of the followings are true (false) in the set of real numbers? A) (Vx) (y) (x+y=10) B) (3x)…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.