B and C are sets of real numbers defined as follows. B={v|v<3} C={v| vz가 Write BnCand BUC using interval notation. If the set is empty, write Ø. (0,0) (0,0) (0,0) BnC =0 [0,0) Ø OUD BUC = I 00 - 00 Start over

Q: express the set of numbers x satisfying the given condition as an interval.       I x+ 7 I &lt; 2

A: Given: x+7&lt;2 We know that solution of inequalityx+a&lt;b is given by -b&lt;x+a&lt;b

Q: If x, y and z are three real numbers such that x+ y+ z= 4 and x + y + z = 6, then show that each of…

A: Introduction :

Q: Prove that the interval (0,1) ⊆ R is equinumerous with the interval (3,7), where R is the set of…

A: To establish a one to one  , onto (bijective map) between the open intervals (0,1) and (3,7)

Q: Come up with an open interval A and closed interval B such that A U B = (0,4) and A (upside down U…

A:

Q: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A: We need to find x and y.

Q: onsider (G,*) where * is defined as a*b3Da is the set of all non-zero real numbers

A: Let  G=ℝ-0For a,b∈G⇒a*b=ab2a,b∈ℝ-0⇒ab2∈ℝ-0a*b∈G   The closure prosperity For…

Q: Let the domain of x be the set of real numbers. Then Vx, (–+1 € R) is O a true statement O a false…

A: Let the domain of x be the set of real numbers.

Q: Assume that a and b are real numbers such that a <b. Prove that the interval (a,b) is an open set.…

A: Given that a and b are real numbers and a&lt;b. Prove that (a,b) is an open set

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

A:

Q: Let R, - {r E R|1 5 x3 x < 1 for each positive integer i. (Enter your answers using interval…

A:

Q: Describe the set of real numbers satisfying Ix - 31 = Ix - 21 + 1 as a half-infinite interval.

A:

Q: 1a. Show that for the closed interval [a, 6], its set of interior points is the open interval (a, b)…

A:

Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that xn > y

A:

Q: Show that the interval [a,b] is complete

A: Given

Q: Find a set B that is well-defined such that 10 ɛ B and 5 ɛ B. B = {x|x ɛl and x < 11}, I the set of…

A:

Q: C and D are sets of real numbers defined as follows. C={v|v>4} D-{v| v

A: C ∩ D those element contained in both C and D. C U D those element contained either in C or D

Q: 33. Let R be the set of all real numbers, x ER and n eN a n 2 2. If (1+ x) > 0, then which of the…

A: Option (C) II only is correct.

Q: Prove or disprove: If x and y are real numbers with y 2 0 and y(y + 1) < (x + 1)², then y(y – 1) <…

A: We have to prove or disprove that if x and y are real numbers with y≥0 and yy+1≤x+12 ,then yy-1≤x2.…

Q: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A:

Q: _The Cauchy-Schwarz Inequality states .+ a%)(b} + b3 + ...+ b,) (a,b1 + azb2 + ...+ a,bn)? < (aỉ +…

A: Given

Q: R.1. Use the Schröder-Bernstein Theorem to prove that the intervals [0, 1) and (1, ∞) on the real…

A: The trigonometric tangent function sprang to mind first, and a strategic linear transformation of…

Q: Let the domain of x be the set of negative real numbers. Then Vx, (1+ x² > 0) is a true statement a…

A:

Q: Let a and b be non-negative real numbers with b+ 0 and p,q > 1 and+= 1, then a show that ab <+

A: Define a function y : [0,∞)→ℝ by yt=1q+tp-t1p, for every t∈ [0,∞). Now differentiating,…

Q: 1. Show that the distance between two numbers in the real number line, given by d(x,y)=|x-yl,…

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

Q: a Prove that the interval [-1, 2] is a closed set in R. Explain each step in your argument.

A:

Q: express the set of numbers x satisfying the given condition as an interval.          I 4x - 1 I ≤ 8

A: 4x-1≤8

Q: Let R be the set of real numbers, A = {x € R: 5<x< 10}, B = {r e R: 7<x<20}, C = (0, 10], D= (9,…

A:

Q: (a) Let S be a set of real numbers with the property that if x1, x2 € S, then the midpoint (x1 + x2)…

A: a) Let S be a set of real numbers with the property that if x1,x2∈S, then the midpoint 12x1+x2 also…

Q: Describe the set S = { x : I 1/2x - 3 I &gt; 4} in terms of intervals.

A: S=x : 12x-3&gt;4

Q: Show that the equality [r + y] = [2] + [y] is not valid for all real numbers r and y.

A: Consider the provided question, We first define ceiling function. The ceiling function maps x to the…

Q: Let R, = = 1, 1 + for each positive integer i. (Enter your answers using interval notation.) (a) 7…

A:

Q: 11. The set of all pairs of real numbers of the form (1, x) with the operations (1, y) + (1. ")=…

A: Given: The set of all pairs of real numbers of the form 1,x with the operations  1+y+1+y'=1,y+y' and…

Q: Let x and y be real numbers. Disprove: If |x| < |y| then |x+1|< |y+1]. Let x, y, and z be real…

A:

Q: express the set of numbers x satisfying the given condition as an interval.       I 3x + 5 I &lt; 1

A: To solve the inequality: 3x+5&lt;1 Solution: We know that if x&lt;a then -a&lt;x&lt;a. We have…

Q: Z is the set of integers, R is the set of real numbers. 1) Functions f, g, h are defined as f: R ->…

A:

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: Let R be the set of real numbers, A {x e R: 5<xs 10}, B= {x e R: 75x< 20}, C= (0, 10], D- (9, 15), E…

A:

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: If x and y are real numbers and x>1, prove that there exists a positive integer n such that x" > y

A:

Q: A and B are sets of real numbers defined as follows. A={v| v7} Write A N B and A U B using interval…

A:

Q: If an inflection point of the aurve f(x)=acos(2.x) +bsin(3x) is P(z/6,5), then what are the real…

A: At inflection point :   d2dx2fx=0d2dx2acos2x+bsin3x=04acos2x+9bsin3x=0

Q: Suppose x is a real number. Prove that if x 1 then there is a real number y such that y+1 = x. 4-2

A:

Q: 6. Prove that |x.y| = |x|.|y|, where x and y are real numbers.

A:

Q: Prove that if a and b are real numbers with a < b, then there are infinitely many rational numbers…

A:

Q: Describe the set S = { x : I } x - 3 I &gt; 4} in terms of intervals.

A: S=x : x-3&gt;4 Now consider, x-3&gt;4⇒x-3&lt;-4  or  x-3&gt;4   ∵x&gt;a⇒x&lt;-a  or  x&gt;a⇒x&lt;-1…

Q: Express the set W = {x| -6 < x < 1} using interval notation. Box 1: Enter your answer using interval…

A:

Q: Prove or disprove: If x and y are real numbers with y ≥ 0 and                           y( y + 1) ≤…

A: Given equations - yy+1 ≤ x+12             ....................(1)yy-1 ≤ x2…

Q: Prove the implication: For all real numbers x and y if x + 2y > 42, then x> 21 or y > 10.5.

A: The solution are next step

Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

A:

Q: Let z and y be real numbers. Prove that, if 5æ + y > 11, then z> 2 or y > 1.

A: