1) Show: P(E) ≤ P(F) 2) Show: P(E) is a subset of P(F)

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

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

A:

Q: If f is [Select] f(x) > [Select] [Select] on (a, b) and f(x) #0 for all x in (a, b), then either for…

A: This is a question on the properties of continuous function.

Q: Suppose f : N → N has the rule f(n) = 4n + 1. i) Determine whether f is 1-1. Justify your answer…

A: ,

Q: Show that if a < c< b, then fave (a, b) = () fave l(a, c) + C - a | favg [c, b]

A: Solution...

Q: a) Prove that P(EUF) ≤ P(E) + P(F).

A: Given that Prove that P(E U F) ≤ P(E) + P(F)

Q: Ex. Show that [b, c) ~ [a, o), where a, b, c ER and b< c. [H7-9]

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Q: If B C A, then (i) P(AB)=P(A) - P(B), (ii) P(B) ≤ P(A)

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Q: Suppose P(A) = 0.4 and P(B) and B, show that 0.1 ≤ P(An B) ≤ 0.4. = 0.7. With no other assumptions…

A: We have given thatP(A) = 0.4P(B) = 0.7We have to show that0.1 ≤ P(AB) ≤ 0.4

Q: By using the fact that P[AU B] 1 –Ei=, P[A£].

A: (a). Prove that P [A U B U C] ≤ P[A] + P[B] + P[C]: It is given that P [A U B] ≤ P[A] + P[B]. The…

Q: Let (A,) be a poset. Define a function f: A → P(A) by f(x) = {a € A: a <x}. What can you say about x…

A: Here given that be a poset.Define function is  by Noted that here  is power set of  .Here we have to…

Q: Let X-x²(18). Given P(7.015 < X <)-029th - then: a) 14.44 b) 10.865 c) 6.265

A: Let X~χα2( 18). GivenP(7,015 &lt;X&lt;χα2)=0.29To find the χ2(α) using the Excel software…

Q: Let F(x.y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

A: The symbolic is given as follows: ∃x∀y¬Nx∧Wx∧Ry→¬Fx,y We are given that: Fx,y: "x is friends with…

Q: Let f(z) be a rational function with no poles on the positive real axis, and suppose that lim Pf(z)…

A: As per the question we are given an importer integral and we have to find a generalized formula to…

Q: - If C is Convex set ond a GR, then XC is a Convex set

A: Let C be a convex set and x∈R Then we have to show that xC is a convex set. The set xC is defined as…

Q: 6. Let 2 be a set and f, g: → R. Assume max{f(x) + g(x) | x = }, max{f(x) |x€N}, and max{g(x) | x =…

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Q: a) Find P(Z > 1.5) [Select] b) Find P(-1.5 ≤Z≤-0.5) [Select ] c) Find P(Z<-1.5) [Select] ◄►

A: Here Z is standard normal variate  i.e. Z has normal distribution with mean 0 and standard deviation…

Q: Is the set {(x1, x2) ∈ R2; 2x1+x2 ≥ 1} convex? Justify your objection.

A: Consider the set      S = {(x1, x2) ∈ R2 : 2x1 + x2 ≥ 1} Let, the points (x1, x2), (x3, x4) be in S.…

Q: Let A = { {a}, {b}, {c}, {d}, {e} } Determine by extension P(A

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Q: define the predicate P(x) ⇔ φx(x) = 1. show that P(x) is not computable

A: Given: The predicate  is defined as , where  is the partial computable function computed by the…

Q: Let X be a set (P(X),Δ,∩) where  P(X) is the power set of X, and Δ is the symmetric difference. Does…

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Q: Suppose that P(A) = 0.1, P(B) = 0.3, and P(A|B) + P(B|A) = 0.8. Find P(A ∩ B).

A: From the information, given thatThe formula of the conditional probability, for any two events…

Q: Prove that P(Sn T) P(S) n P(T) for any sets S and T

A: Let, S and T be a any set. also, P(S) be any power set of S and P(T) be any power set of T.x∈P(S∩T)…

Q: let f and g be two bounded read - valu ed functions on the set ASR Showthat sup CPCX) +g X))s…

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Q: For a given data set the Sum of Squares is 212.69 and the sample size (n) is 11. What is the…

A: Given that  Sum of squares (SS) = 212.69 Sample size (n) = 11   We know that  Variance (S2) = SSn-1…

Q: Let X = the integers. Let Y = {0, 1, 2, 3, 4, 5}. %3D Let f : X Y be defined as the remainder when x…

A:

Q: 1) Let f: A ->B with C1 C C2C A and Dic D,CB Which is true? a) f(C) c f(C2) OR b) f(C2) c f(C:) (i)…

A: Given: i) To prove that answer is correct. ii) To give a counterexample to show that the set…

Q: Example: Let x=1,2,3,4,5 15 P(x) = show that p(x) is p.d.f elsewhere

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Q: Give an example of a closed subset S of R2 such that conv S is not closed.

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Q: Let X be a set (P(X), Δ,∩) where P(X) is the power set of X, and Δ is the symmetric difference. It…

A: Unity: Let R, +, ∘ be a ring. If the semi-group R, ∘ has identity element then it is called as unity…

Q: Let f(x) := x² for x∊R, and let E := {x∊R : -1≤x≤0} and F := {x∊R : 0≤x≤1}. Find the sets E\F and…

A: Given, f(x) := x² for x∊ R,  E := {x∊ R : -1≤x≤0} and F := {x∊ R : 0≤x≤1}.

Q: Suppose that A, = {-n, -n + 1,..., –1,0,1, ...,n – 1, n} for any natural number n (note that Ao =…

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Q: Discrete Mathematics: Prove that for all real numbers x, y, and z, if x + y + z ≥ 3, then either x ≥…

A: We will prove by method of contradiction

Q: (1) Let A = {1, 2, 3, 4}, B = {2, 4, 6}, C = {1, 3, 5} and U = {1, 2, 3, 4, 5, 6, 7}. Compute the…

A: By the authoring guidelines of Bartleby, we can answer only first three subparts, please post other…

Q: Supppose that X ~ N (2; 3). Find P (1 &lt; X &lt; 4).

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Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).