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

Q: A population consists of 4 units with values 156, 149, 164 and 155 respectively. Draw all possible…

A: Given that Population size N = 4 Sample size n = 2 Then possible samples WOR are NCn = 4C2 = 6

Q: Let (X, F) be a о — algebra , and be two probability measures on (X, F) so that both are ergodic for…

A:

Q: EX: Show that the telation ? >' is PartiaL oldering set of Por R-

A:

Q: Find yas a fon chenof x if t. %3D with

A: This is cauchy euler equation and we will solve it by changing the dependent variable

Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

A:

Q: Determine whether is a linearly independent set of vec- 3 11 tors in R3.

A: A set of vectors v1,v2,v3,…,vk in a vector space is said to be linearly independent if…

Q: (d) Show that {^} is not an adequate set of connectives.

A: (d) These are necessary and sufficient conditions for a set of connectives to be adequate. If a set…

Q: Let (X, F) be a о — algebra , and be two probability measures on (X, F) so that both are ergodic for…

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Q: show that (0.1)with usual topology is connected

A: Sol

Q: Find the aven bounded by y=x and y =x+2

A: First draw the graph of the function and find the intersection point of the graph:

Q: What is the Squeeze Play Therom

A: Squeeze Play Theorem: Let f, g & h be real functions such that fx≤gx≤hx for all x in the common…

Q: find rank(AT) and nullity(A)

A: Rank of A = rank of A^T use this relation

Q: Let (x, eA) be a measurable space, £: X (-∞, w) and 9:* (-∞0, ∞o) are measurable. Prove that the…

A: Given that X,A is a measurable space. The objective is to prove that the sets  {x∈X:f(x)<g(x)},…

Q: : Does fcz) = Continuous af cis

A: We have to solve given problem:

Q: Find the ared of the reyion R bound ed.by and the liney=x+2 2. 2. =y-yand the line y--x ......

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Q: give example is not To-SPace about to folegical SPace

A: We have to find a topological space which is not t0.

Q: Let D={(txy.2) : x²ny2sz²s 324, z2 Evaluate z dv.

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Q: Show the the Sar induce

A: According to the given information, it is required to show that equivalent norm on a vector space X…

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: let (RiZ) be the usual top on et B-1 ineN] Find B.

A:

Q: Prove that MSE(Ô) = V (ô) + [Bias(Ô)]²

A:

Q: Suppose S and T are balls with the same center. Show that one of them must be a subset of the other.

A: It is given that S and T are balls with same center. Let the center of the balls be a. Assume that…

Q: b)use Cauchy Schwarz inequality to show that if Let u = and v = inequality to show that a² + b?

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Q: Describe the largest set S on which it is correct to say that fis continuous. AX, y) = In(1 + x² +…

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Q: Let S be a non-empty open subset of R that is bounded above. Show that sup S exists but that max S…

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Q: Find the deriratire of y tanx usim the Difinition Rule

A: Given that:y=tanxTo find its derivative.

Q: Let X be the amount of soda released by a soft-drink dispending machine into a 6-ounce cup. Assume…

A: Given information: σ=0.25 a)  P-value for the quantity, where no more than 0.5% of the releases…

Q: Show that Let ECR" is measurable set. If µ(E) >0, then E have a non-measurable subset

A: Here, we introduce the notation Gr :=G∩[0, r) + 1-r ∪ G∩[r,1) - r for G⊂[0,1) and r∈R. Note that…

Q: Let Evaluate z dv.

A:

Q: Let (X, F) be a о — algebra o - , and be two probability measures on (X, F) so that both are ergodic…

A: Let (X,ℱ) be a σ-algebra and μ≠v be a two probability measure on (X,ℱ) So that both are ergodic for…

Q: B. If f = x²cosy + y²sinx then show that fry = fyx ух

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Q: 2. Explain why there does not exist a measure Space (X,S, M) with the pro porty %3D

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Q: (3) In R² with the standard topology: {(x, y) | x² + y² {(x, y) | x² + y? > 1}. = 1}, {(x, y) | x² +…

A: In a topological space R2with standard topology. A  subset O is open if at each point x in O there…

Q: 24. Find the Fowrier r fas - -IN X

A: Hv

Q: Let S be a set of negative numbers. Prove the least upper bound of S cannot be positive.

A:

Q: Prove using Venn diagram that An (B U C) = (A n B) U (A n C)

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Q: for Gib E IR aith ach, let (fa) be a seaj. of diffenntible functions on [a,6]. Suffere (fu) and (fú)…

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Q: Suppose that X,X, are both the open subsets of X, X = X,UX,, and both X and X,NX, are path-…

A:

Q: Prove: le* a. ſ csch x = In - |+c lex+1

A: As per Bartleby guidelines rule I am answering only first question as Both question is not subpart…

Q: let FC k be a Galois extension with Gal

A:

Q: a nonempty compact set of IR. sup Ke K. be

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Q: Show that both ℝ and ℝ2 may be covered by countably many open balls

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Q: ntin

A: It is given that,  If g is continuous and ∫-28g(x)dx=30 We have to find ∫-144g(2x)dx=?

Q: Show that R3 is spanned by S = {(1,1,1), (1, –1,0), (0, 1, – 1)}

A:

Q: Suppose {u,..., 4,, W1, ..., W,} is a linearly independent subset of V. Show that span (u;)…

A:

Q: Let X = {a, b, c, d, e} and let T ={X, Ø, {a}, {c,d}, {a,c,d), {b,c,d,e}), therm %3D O (X,T) is…

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Q: Let S = {2x, 1 – x, x² + x – 1,x + 1,x – 2}. Then %3D P3 P2

A:

Q: -. Show that both R and R2 may be covered by countably many open balls.

A: Soution.

Q: If e-ispure imaginary W hat Restriction is placed on z?

A:

Q: 4.2 Let Fj, be a closed set for k = 1,2, ... ,n in (S, d). Show that U Fk is closed.

A: