Answered: Prove that a finite union of countable…

Prove that a finite union of countable sets is countable. Therefore, if A is uncountable and B ⊂ A is countable, then A \ B is uncountable.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.1: Sets

Problem 26E

See similar textbooks

Related questions

Q: A team physician has determined that of all the athletes who were treated for minor back pain, 72% r...

A: Let the number of athletes be 100. The Venn diagram can be obtained as shown below: The number of a...

Q: lim (x,y)→(0,0) x² + sin?(y) x² + y?

A: Given: lim(x,y)→(0,0) x2+sin2(y)x2+y2

Q: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high t...

A: Given that the highest temperature for the day is 77 degrees and the lowest temperature is 63 degree...

Q: Explain it early and correctly with clear steps by steps

A: Consider the table, which is given in the question. We have to approximate 1125∫0125Ttdt, by left Ri...

Q: 3. a) Negate each and b) tell if the negation is TRUE or FALSE 1. Some bears are brown. 2. All integ...

Q: Explain early and correcty with clear steps by steps

A: From the table, Given, x0=0, x1=20, x2=44, x3=60, x4=90, x5=110, x6=125f(x0)=70, f(x1)=130, f(x2)=...

Q: Real Analysis, I need help

A: A sequence xn converges iflimn→∞xn=l. If this limit does not exist then the sequence diverges. Given...

Q: . If f : R → R is a function, then we write limx→a f(x) = L to mean:∀ > 0 ∃δ > 0 ∀x ( (0 <...

A: Negation for the given definition of limit is to say that there doesn't exists any limit for every δ...

Q: (i) Answer the following question.

A: To prove that a statement P(n) is true by mathematical induction. First of all ,we are to show that...

Q: On an elliptic curve E in the group F37F37 the point P is (21,23). What is the point -P? Select on...

A: According to the given information, it is required to determine the point -P where P is (21,23) on a...

Q: 7. Let f(x) = 2x +3x2 - x- 5. Without forming the divided difference table, determine f xo, x1, X2, ...

A: Let f(x)=2x3+3x2-x-5. Without forming the divided difference table ,we have to determine fx0,x1,x2,x...

Q: Need answers C Only C required

A: Simpson's rule is exact for a cubic function.

Q: derive formula for the volume of a Truncated tetrahedron and a Truncated cube Truncated tetrahedron:...

A: To derive: Volume of truncated tetrahedron, V=23122a3 We know, the volume of the truncated tetrahedr...

Q: I need help with putting this matrix into Reduced Echelon Form, showing all the steps.

Q: 15.These drawings have the same shape but different sizes. They have proportional side length, point...

A: Consider the provided question, We have to determine the given statement is defined which term. A. S...

Q: A chemist has two alloys of bronze, one that is 12% tin and 88% copper, and a second that is 10% tin...

A: Given, 12% tin and 88% copper in alloy 1. 10% tin and 90% copper in alloy 2. Consider 100 g quantity...

Q: Let a and b be elements of a group. If |a| and |b| are relatively prime, show that <a> inters...

A: Let m and n be the order of the elements a and b of a group G. Given that the orders of a and b are ...

Q: Problem 1 Solve the following differential equations by using power series solution around singular ...

Q: Do you understand this?

A: First we will answer all questions which are completely visible or complete questions.

Q: I need help doing these. Question on the page. Thanks

A: 17. V=13Bh To solve for h proceed as follows Multiply both sides by 3 3V=Bh Divide both sides by B 3...

Q: Use ratio and proportion to solve the following business situation. Suppose a local office store has...

A: Given: A press that can print 54,000 brochures per hour. Calculation: Obtain the number of brochures...

Q: Find the Fourier series for f(x) = x³. If you differentiate your series, do you re- cover the Fourie...

A: The given function is f(x)=x3 The formula for the Fourier series is given by f(x)=a0+∑n=1∞ancosnx+b...

Q: Ali and Kiana buried a treasure together on their school’s field. Ali made an 8-inch-wide map to rec...

A: Consider the provided question, Since, Ali map is 8 inch wide. This 8 inch wide map represents the f...

Q: Please solve the screenshot and explain the steps. The answer is *not* 104.718 as the prior responde...

A: Let's find the triple integral, ∫∫E∫4x dv, where E is bounded by paraboloid x=5y2+5z2 and the plane...

Q: Advanced Math Question

A: The objective is to negate each given statement and check whether the negation is true. For a: Consi...

Q: Consider the Euclidean vector space R with the dot product. A subspace UCR° and z e R³ are given by ...

A: From the given U, let, u1=0-1202,u2=1-31-12,u3=-34121,u1=-1-3507

Q: Show that, for a function f(x) with anti-derivative F(x), d s)ds f(x). %3D dx a

A: Suppose f(x) has an anti-derivate F(x), v(x) and u(x) are differentiable, then Leibniz's rule of dif...

Q: Briefly explain the meaning of the following terms. Provide at least one relevant example • Central ...

A: CLT is useful in evaluating the relation between the sampling distribution of the sample means and t...

Q: Define the binary operator ⊗⊗ by: a⊗b=a2+b+5a⊗b=a2+b+5 Find each of the following: 7⊗4=7⊗4= ...

A: Given binary operation is a⊗b=a2+b+5

Q: Solve for the base (in $). Round to hundredths when necessary. What is the base if the portion is $4...

A: Consider that the value of the portion is $4570 and the value of the rate is 55%. Transform percent ...

Q: Find the average height of a hemisphere z=sqr( 4-49x^2-49y^2 ) above the disk x ^2+ y^2 ≤4/49. The a...

A: Given that z=sqrt(4-49x2-49y2) above the disk x2+y2≤4/49. z=49449-x2-y2 then we know that 49=7. z=74...

Q: (d) dln

A: Without loss of generality, we can substitute d and nd in the above expression ∑d|nσ(d) ϕ(nd) = ∑d|n...

Q: A 2000 L tank initially contains 40 kg of salt dissolved in 1000 L of water. A brine solution contai...

A: Set up a differential equation. Let Q(t) denote the amount of salt in the tank at a time t. The tank...

Q: x sin(y) lim (x,y)→(0,0) x² * + y

Q: Simplify the following expressions.

A: 1. Given: 96x2+32-71x2-9y+7xy-24-3xy+4y+5y On arranging the like terms together, we get 96x2-71x2+32...

Q: Q1. Find (i) the Fourier cosine series and (ii) the Fourier sine series of the function f(x) = x, 0 ...

A: To find the Fourier cosine series, assume the function as even so that the graph of the function wil...

Q: Negate the following statements a) ∀ x ∃ y P(x, y) ∧ ∃ z R(x, y, z) b) ∀ x ∃ y P(x, y) → Q(x, y)

Q: Advanced Math Question

A: Consider the given graph. The graph represents the function y=fx. We have to evaluate the limit limx...

Q: Q (3): Given the field D = p sin 0.5o a, + p cos 0.50 a, +pa, C/m, evaluate both sides of the diverg...

A: According to the formula of divergence theorem, I=∫∫V∫div V dv=∫∫∫∂Vρ∂ρ+∂Vϕ∂ϕ+∂Vz∂zdρdϕdz Now calcul...

Q: Suppose f is a continuous function with x = a in its domain. Part 2 of the Fundamental Theorem of Ca...

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified. ...

Q: A ping pong ball is drawn at random from an urn consisting of balls numbered 2 through 10. A player ...

A: a) The possible numbers on the ball are: 2,3,4,5,6,7,8,9 Even possibilities= 5 Odd possibilities= 4

Q: (16) Give an example of two nonisomorphic 2-regular graphs of the same order and show that they are ...

Q: let n>=2 be a natural number Let V be the set of people in a party of n people. Use set-builder ...

Question

Prove that a finite union of countable sets is countable. Therefore, if A is uncountable and B ⊂ A is countable, then A \ B is uncountable.

Expert Solution

Step 1

First of all we have to prove that,

The union of countable family of countable sets is countable.

PROOF:

Without loss of generality, we can denote a countable family of sets by $A_{1}, A_{2}, A_{3} \dots \dots \dots \dots$

Suppose $a_{i 1}, a_{i 2}, a_{i 3}, \dots \dots \dots$ is an enumeration for $A_{i}$ . Then,

$Y_{i = 1}^{\infty} A_{i} = {a_{i j} : i \in ℕ, j \in ℕ}$

To the element $a_{i j}$ we assign a natural number $n$ so that there corresponds at most $n - 1$ distinct elements of A.

Therefore, A is countable by Countable Lemma.

Step by step

Solved in 2 steps

Knowledge Booster

$Finite State Machine$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.