5

2 Show: If A is measurable, B € A,and m(B) = 0 then m(A) m(AI B)...

Question

2 Show: If A is measurable, B € A,and m(B) = 0 then m(A) m(AI B)

2 Show: If A is measurable, B € A,and m(B) = 0 then m(A) m(AI B)



Answers

Prove that for any integers a, b and c if c|a and c|b then c divides any linear
combinations of a and b

Question and this. We need to prove or disprove. The P. He crossed. Be equal to be a grass B. B. We have to prove all this probe. Okay? Now let us zoom. Mhm. E. To be M. And be to the end. So from here, B. A. Will be equal to tourists. To the power. Um And B. B. Would be equal to to raise to the power hand. So right inside would be equal to be a Class B. B. Okay. These are the numbers that's where Modelers E. Gross B. B. Would be equal to tour is to the power M. Into uh to raise with the power in to raise to the power um into to raise to the power. And so to restore power M. Pleasant mm left hand side. Let us get the value of A. N. B. First E. N. B. That is M into end. To be a Crosby would be cool to to restore the power. I am aiming to end. Okay. And from here, from both both of these exhibitions, we can see that to raise to the podium. Plus in equal to tourists. The power aiming to end, which is not possible because M plus N. Cannot be equal to mm two. And so it is not true. It is disproved. Thank you

We were given the capital omega com api is a finite probability space and that F is the power he said. That is the set of all subsets of omega. First, we'll show that for any random variable X X is F measurable. And then we'll show that the conditional expectation affects given death would equal X itself. Now suppose X is a random variable that is X is a function from capital. And we got to the set of reels. Now for any boils that be over the reals, X inverse B is the set small omega in capital omega. Such that except omega is in B which is clearly a subset of omega. And so must be in the power set S that is X inverse B is an element of F which shows that X is F measurable. Now note that the conditional expectation of X given F is defined as a random variable that satisfies the following two properties number one expectation of X given F is a F measurable random variable and number two or any A N. F. The integral over a of expectation X. Given F. With respect to the probability measure he closed. And to grow over A of X with respect to the probability measure here we have that X itself is an F measurable random variable. Moreover, it trivially satisfies property too. And it's tribute that is trivially true. That integral of way of X with respect to B is equal to the integral over A of X with respect to be So x here satisfies both properties one and 2. And so expectation of X given ETh equals X. Here is important to note that this equality holds almost everywhere. That is, and he set where the conditional expectation X given it does not equal to X has probability measure zero. That's it for this problem.

In this problem of relation in France. And let's start with the binary operation. So here this is binary operation on end. So this is on end. We have defined given set end and the city find that is to be is equal to a safe of A. And we at cf of A. And B. And now we have to check for star is associated or competitive. And also we have to find the identity if possible. So first we will check for associated property. Since this is binary operation, that means a. Star B is equal to be star. And this is the condition for a property or we can say or for operation to be here competitive. So this is competitive competitive property. And now we have to check for associated so A Star B. The stars see should be equal to A star the stuff see. So maybe that means this is it safe of A. And we so we say that at C F F A n B, so at C F of A and B. And it starts see and now here this would be F C F. So here is our first, so that's what we ate there. And then this will be at cf of B and C. And from here we say that this means that safe of a BNC at cf of A B N C. And from here we say that at cff A B and C. From here, let's see. F A B C C. So that's why. So this would be, so that's why electricity close to a ridges. So L. Z. Is equal to Rhs. So hence we say that this operation Star is yeah. Associated. Associated. So this is this operation is competitive and this associative also. And now we have to check for identity element. No, as we know that here one star E. And this is equal to a star one, where this is not equal to itself. So that's why there doesn't exist any other elements. So there is no identity element, identity element. So this is the answer.

To do this proof. First you have to understand the definition of X divides Y. So X divides Why if there exists an integer D. Such that D times X equals Y. Now it's really important that it's an integer because if it was a fraction then it wouldn't be true. Okay, so for example seven divide 63. 6 cents. There exists an integer D. And in this case D equals nine. Not A equals nine. Such that nine times seven equals 63. But seven doesn't divide 80. Since there's no integer D. Such that D times seven is 80. There is a number but that number is not an integer. That number is a rational number, 87th whatever that is. Okay. And then linear combination of A. And B means X times A plus Y. Times B. An X and Y. Are imagers. Okay, so here's what you're trying to prove. If she divides A. And see divides B then see divides X. A plus Y. B. Okay, proof. So first you always say what each one of these things means. Sea divides A. If there exists an inter juror, Let's call it the one such that see time's D. One equals A. Okay. And then see divides be if there exists and into juror It's called D two. That's such that. See time's D. Two equals B. Okay, so now we know what we're given. So then start with the thing you're trying to show it divides into start with this then X. A plus Y B equals. Now what you're gonna do is use the substitution property in place of a. You're going to put this this right here. That's a in place of B. Going to put this right here. Okay. So we have mm X times C D one plus Why times C D two. All right then then not the eraser then you can factor C out of both of those ex D one plus Y. D two. Okay. Okay. Now X is an integer. D one is an integer. Why is an integer? D two is an integer. When you multiply integers you get an integer When you add in angers you get an integer. So xd one plus Y D two is an integer. So let's call em where M equals X D one plus Y D two and M is an integer. How do I know it is an injured. Okay. Well I just said it was but because or since into jurors since let's be more specific. The set of into jurors is closed under multiplication and edition can close means when you take two of them and you do that thing to them. The new thing you get is also an integer. Okay. So I took two integers. I multiply them together. I get an integer. I have two integers. I added them together. I get an integer. Okay, now I'm done. Okay. Here's how I know I've shown that this thing equals an integer time. See so see divides X A plus Y B. A linear combination of A and B. Okay. Every single divides, by proof works the same way. Okay? You always say what they gave you. You start with the thing. You're trying to divide into. You use substitution and it magically turns out to be what it's supposed to be. Okay. Hold that helped.


Similar Solved Questions

5 answers
I08:Fmks OSQLL4Y 2018 12019 19. ir: 2+4 Jik Suppose - (ae+) that has binomial any given trial. Find distribution based the approximate 100 trials with probability P[15 < X < 25] probability of success of .2 on using the integer correction .
i08: Fmks OSQLL4Y 2018 12019 19. ir: 2+4 Jik Suppose - (ae+) that has binomial any given trial. Find distribution based the approximate 100 trials with probability P[15 < X < 25] probability of success of .2 on using the integer correction ....
5 answers
Cos(0 + cOsI {(20 cOsI 30 cos(40 cos(50 +Problem 5. (15 points) Let BaId *Find a,b,c € R such thatBx aXPlease express b, aud in teTms of 0 and 0
cos(0 + cOsI {(20 cOsI 30 cos(40 cos(50 + Problem 5. (15 points) Let B aId * Find a,b,c € R such that Bx aX Please express b, aud in teTms of 0 and 0...
5 answers
Examine the labeled bonds in the structures below and determine the relative strength and length for each row;StructureWhich bond is weaker?Which bond is longer?(Choose one)(Choose one)
Examine the labeled bonds in the structures below and determine the relative strength and length for each row; Structure Which bond is weaker? Which bond is longer? (Choose one) (Choose one)...
5 answers
Refer to Exercise $43,$ and determine the minimum temperature to which the balloon described in part(b) would have to be heated before it could begin to rise in air. (Ignore the mass of the balloon itself.)
Refer to Exercise $43,$ and determine the minimum temperature to which the balloon described in part (b) would have to be heated before it could begin to rise in air. (Ignore the mass of the balloon itself.)...
5 answers
Find the point of intersection of the lines $x=t, y=-t+2$ $z=t+1,$ and $x=2 s+2, y=s+3, z=5 s+6,$ and then find the plane determined by these lines.
Find the point of intersection of the lines $x=t, y=-t+2$ $z=t+1,$ and $x=2 s+2, y=s+3, z=5 s+6,$ and then find the plane determined by these lines....
5 answers
Questicn 4pes0.20 mol of NaF Is addcd to 1.00 of 0.35 M cadmium nltrate; CdINO3)z: Which of the following statements is correct? Ksp 6.44 * 10 3 for CdFz0 Cadmium (luoride precipilates.0 The solution unsaturated and no precipitate forms increased by the presence additional fluaride ions The solubility of cadmnium fluoride nilrte make meaningful prcdictions this system; One must know Ksp for cadmium0 The presence of NaF will raise the solubility of CdNOglz
Questicn 4 pes 0.20 mol of NaF Is addcd to 1.00 of 0.35 M cadmium nltrate; CdINO3)z: Which of the following statements is correct? Ksp 6.44 * 10 3 for CdFz 0 Cadmium (luoride precipilates. 0 The solution unsaturated and no precipitate forms increased by the presence additional fluaride ions The solu...
5 answers
Describe and explain in a paragraph of no more than 250 wordsthat differentiate the growth of herbaceous plants from the growthof trees and shrubs. Also, state what is the basis of thedifferences. Remember that it should be an answer formulated in theform of a paragraph, preferably a maximum of 250 words, with fairlyformal and precise writing in terms of concepts. You must useAPA-style citations and references.
Describe and explain in a paragraph of no more than 250 words that differentiate the growth of herbaceous plants from the growth of trees and shrubs. Also, state what is the basis of the differences. Remember that it should be an answer formulated in the form of a paragraph, preferably a maximum of ...
5 answers
If the maximum clear distance for @ man is 4 m; then the strength of tha lens required to correct the vision in diopter is104b.-0.51c35d -25
If the maximum clear distance for @ man is 4 m; then the strength of tha lens required to correct the vision in diopter is 104 b.-0.51 c35 d -25...
5 answers
QUESTION 10For the following theoretica reaction; calculate tne theoretical yield. Enter the numerical value to 3 decimal places: Do not include units (g) (Please note; the numbers have been changed relative to the handout )Reactant Reagent X Product Solvent; TemperatureCompound Reactant Rearent X SolventAmount Mole Ratio 0.625 1.0Molar Mass 160.24g /mo 310.32 E mol40 mLActual yield: 0.609 g; Product molar mass 232.75 g/mol
QUESTION 10 For the following theoretica reaction; calculate tne theoretical yield. Enter the numerical value to 3 decimal places: Do not include units (g) (Please note; the numbers have been changed relative to the handout ) Reactant Reagent X Product Solvent; Temperature Compound Reactant Rearent ...
5 answers
977pointe_LarsoneT5 4.6.025 Moted Yout Analyze and sketch graph of the function. Find any Intercepts_ relatlve extrema_ points of Inflectlon, and asymptotes (If an answer docs not exist, entcr DNE: )intercepts(Y) (y)) (smaller x-value) ) (larger x-value)relative minimum relatlve maxlmum point of Inflection (xY)Find the equation the asymptoteUse graphing utillty to verily Your results:Nood Holp?
977pointe_LarsoneT5 4.6.025 Moted Yout Analyze and sketch graph of the function. Find any Intercepts_ relatlve extrema_ points of Inflectlon, and asymptotes (If an answer docs not exist, entcr DNE: ) intercepts (Y) (y) ) (smaller x-value) ) (larger x-value) relative minimum relatlve maxlmum point of...
5 answers
Proplemmbi(1 point) Match each kectonmeld with Its [email protected] G(r,y)KahEdPIF(I,y) KkHkEERER H(z,y) 04 4jD 8W
Proplemmbi (1 point) Match each kectonmeld with Its graphi @H G(r,y) KahEd PI F(I,y) KkHkEE R ER H(z,y) 04 4j D 8 W...
5 answers
Question 33014p13Match the chemical reaction that is closest to the acid base definitionArrhenius(Choose ] [choose HCI+ HzO H3O - NaHco3 H2cO3 NaF NHS BF3 NH3BF3Bronsted-LowryLewis[Choose
Question 33 014p13 Match the chemical reaction that is closest to the acid base definition Arrhenius (Choose ] [choose HCI+ HzO H3O - NaHco3 H2cO3 NaF NHS BF3 NH3BF3 Bronsted-Lowry Lewis [Choose...
5 answers
422.2 micro-Farad capacitor is connected in series with 35 Ohm resistor and a 7.8 Volt battery: What is the total charge on the capacitor 1 time constant after the circuit is completed if the capacitor was initially uncharged?Select one: a. 1211.49 micro-Coulombsb. 3293.16 micro-Coulombsc.34.22 micro-Coulombsd. 2081.67 micro-Coulombse. 2847.48 micro-Coulombs
422.2 micro-Farad capacitor is connected in series with 35 Ohm resistor and a 7.8 Volt battery: What is the total charge on the capacitor 1 time constant after the circuit is completed if the capacitor was initially uncharged? Select one: a. 1211.49 micro-Coulombs b. 3293.16 micro-Coulombs c.34.22 m...
5 answers
KlelibekienslellalmelebhehuSakehkeleBAeleaQuestionii6 Find @issingoco 6i7nf Jatrs MBa No correct answer RUbzNm EkAk HHAMm Hhkeshg
KlelibekienslellalmelebhehuSakehkeleBAelea Questionii 6 Find @issingoco 6i7nf Jatrs M Ba No correct answer RUbzNm EkAk HHAMm Hhkeshg...
5 answers
Halle tal que Tn aproxime K #dx COn ua presicion de 15 digitos_ iQue nuimero irracional esta aproximando ?Halle e polinomio de Taylor de grado 4, Pa(), alredledor de 0 para la funeion y Halle Ia presicion para COn la cual pa() aproxima para valores de _, <I <
Halle tal que Tn aproxime K #dx COn ua presicion de 15 digitos_ iQue nuimero irracional esta aproximando ? Halle e polinomio de Taylor de grado 4, Pa(), alredledor de 0 para la funeion y Halle Ia presicion para COn la cual pa() aproxima para valores de _, <I <...

-- 0.021548--