Suppore that A and B aru Awre set such that (AI= IB1 Show that %3D (P(A), P(B) denote the pouser sets of A& B respictively)

Q: (a, o) is not measurable.

A: to find that a,∞ is measurable or not  proceed as follows We know that every interval is measurable.…

Q: &2/ suppost se =20, 1} and c={208{ fie ld =20,18 and e= Enumerate the class of all 6- Containing C…

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Q: Let A be a set. Prove that S = 0. SEP(A)

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Q: Give example of clsad subset of IR cwhise two an dimeasiunal Lebesque outer masuie ís o

A: Consider the unit square L=0,1×0,1. Clearly L is a closed set with boundaries l1, l2, l3 and l4.…

Q: 4. Give an example of a non-measurable subset of R. (witheutProof)

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Q: Let (A, 3) be a poset, and let BC A. Prove that B has at most one greatest lower bound.

A: Let, A,<~ be a poset and B is a subset of A and a∈A. Then by the definition, a is the greatest…

Q: (ii) for every singleton set A, m* (A) = 0.

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Q: List all of the subsets of (x, y, z).

A: Given that the set x,y,z. Find all the subsets of the given set. Definition: A set is a well-defined…

Q: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: 7. Show that if S x T is a closed subset of R?, then S and T are closed subsets of R.

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Q: for which the giyen system has no

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Q: TION 4 If A, B, C be three sets such that Au B = AUC and ANB = ANC, then : O B = C O A = C O A = B =…

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Q: Suppose is dhe iavene faction of a diffarentiable šunc- tica fand let Glu) -1/r . E3) - 2 and /3) -…

A: G(x)=1f-1(x)f(3)=2 , f'(3)=1/9

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A: The sine distance between two points x,y∈ℝ2 is defined as: dsinx,y=x.yxy and the cosine distance…

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Q: 9) Find the power set of each of these sets, where X, y are distinct elements: (a) {x, y} (b) {x, y,…

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Q: 4 Show that a + B = B +a for all a, BE C.

A: We can write alpha and Beta in general form of element of complex number.

Q: Consider the word TORTOISE. Count the number of arrangements of this word (a) such that no two…

A: We have to solve given problem:

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A: For the given question ,t he first thing to do is to find the value of λ. Then, we will proceed…

Q: 4. Let b > a > 0. Show that (a,b] is neither closed nor open.

A: Explanation of the solution is given below....

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Q: Suppose that N+ 1 balls, of which a+b+1 are red and N-a-bare blue, are arranged in a linear order in…

A: From the given information, There are N+1 balls, of which a+b+1 are red and N-a-b are blue arranged…

Q: If ZH and LJ are supplementary in HJKL, are a) ZK and ZL necessarily supplementary also? b) ZH and…

A: Given :∠H and ∠J are supplementary…

Q: Con sider Sam ple X,, X2,.., Xg from a NC8,4). Find the Coverage Probabilit a of interval [x-2, +2].

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Q: 2, Say whether the Runction is even, odd, or neither. Give reasanS for your dnswer. ga) = x"+ x*-1

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Q: 6. Write down all the set-partitions P of [5] such that for every BEP, if x € B and y EB then lyx ≤…

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Q: 1 A class of 40 students was each required having three textbooks in each of Economics, Mathematics.…

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Q: Prove that the following 2 sets are equal: {4k + 5 : k ∈ Z} = {4k + 1 : k ∈ Z}.

A: Two sets are equal if and only if They have the same element  We are using here if x €A. <=>…

Q: Consider the word TORTOISE. Count the number of arrangements of this word (a) such that no two…

A: Consider the given word TORTOISE. The objective is to count the number of arrangements of this word:…

Q: Let'Y be the set of f bleod types B+ Hat type Connot donate blood to.

A: Here, X is the set of blood types AB- can donate blood. AB- can donate blood to AB- and AB+ Hence,…

Q: If z = eax+by az then a az is ay

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Prove the following idenlity A-V = VA

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Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

A: It is mentioned that 1 in every 10 messages is spam. Hence, the probability that the message is spam…

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A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are,…

A: Given R and S are two Poset on a set X. (1) Consider R∩S. Since R and S are poset, therefore each…

Q: Prove that the set S = {n² : n E N} is denumerable.

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Q: There are two food carts serving food at a local park. At any given time, Let A denote the number of…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Suppose that X is a subset of Y, such that P(Y)>0. Is true or false that P(X|Y) is equal to…

A: It is given that X is a subset of Y This means that PX∩Y=PX...(i) The formula for PX|Y is given by:…

Q: 2. Let S be the set [9]: (1.2.9). (c) List 5 derangements of S having 2 in the 3rd position and 5 in…

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Q: Suppose that a,beG such that a = m and b =n with Gcd (m,n) = 1. Then n | is in mn

A: Suppose that a, b∈G such that a=mb=n and Gcdm, n=1 i.e., m and n are relatively prime. We will find…

Q: 5. Deduce from (4) that the set {2} 2-: n = 1, 2, 3, ... is closed in R.

A: Given set  S =2 ∪2-1n  :  n=1  2,  3 , . . .

Q: Set us the matrix of transition probabilities and show the transition b. Find the steady state…

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