Consider the class C of all intervals of the form (a, b), a, b ∈ R,...

Consider the class C of all intervals of the form (a, b), a, b ∈ R, a < b and ∅. Show that C is closed under finite intersections but not under complementations or unions. Hint: to show closure of finite intersections, it is enough to prove closure for intersections of 2 sets.

Expert Solution

milcah answered 1 year ago

Let X = R and A = {disjoint union of the intervals of the form (a,...

Let X = R and A = {disjoint union of the intervals of the form (a, b], (−∞, b] and (a, + ∞)}. Prove that A is an algebra but not a σ-algebra.

V=[(a b), a,b E R+] with (a1 b1)+(a2 b2)=(a1a2 b1b2)and for c E R, c(a b)=(a^c...

V=[(a b), a,b E R+] with (a1 b1)+(a2 b2)=(a1a2 b1b2)and for c E R, c(a b)=(a^c b^c) is a vector space over R. Define T:R^2 to V by T[a b]= (e^a e^b). prove T is a linear transformation from R2 to V.

Consider a class with 3 sections denoted as A, B, C. Let the number of students...

Consider a class with 3 sections denoted as A, B, C. Let the number of students in section A be 10, in section B be 20, and in section C be 15. Let the score of uniformly chosen student be denoted by random variable X. The student’s section be denoted by the random variable Y where Y = 1 if the student is from section A, Y = 2 if the student is from section B and Y = 3...

Let the schema R = (A,B,C) and the set F = {A → B,C → B}...

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Consider the Potential V(r) =Vo (c/r) exp (-r/c) (where c is a constant) and a deutron...

Consider the Potential V(r) =Vo (c/r) exp (-r/c) (where c is a constant) and a deutron of reduced mass m moving in this potential . (a) Using a trial wave function R(r) = exp (- d *r / c) (d is constant ) find the ground state energy if Vo= 1.35 (b) If one bound state energy is -2.2 find Vo

1. Consider an arithmetic expression of the form a#b=c. Check whether it is possible to replace...

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Consider the relation R= {A, B, C, D, E, F, G, H} and the set of...

Consider the relation R= {A, B, C, D, E, F, G, H} and the set of functional dependencies: FD= {{B}—> {A}, {G}—> {D, H}, {C, H}—> {E}, {B, D}—> {F}, {D}—>{C}, {C}—> {G}} 1) Draw FD using the diagrammatic notation. 2) What are all candidate keys for R? 3) If delete {C}—>{G} and change {C, H}—> {E} to {C, H}—> {E, G}, what are all candidate keys for R

Consider the natural join of the relation R(A,B) and S(A,C) on attribute A. Neither relations have...

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Let R be the relation on Z+× Z+ such that (a, b) R (c, d) if...

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Show that the set of all real numbers of the form a+b sqrt(2)+c sqrt(3)+d sqrt(6),where a,b,c,d...

Show that the set of all real numbers of the form a+b sqrt(2)+c sqrt(3)+d sqrt(6),where a,b,c,d ∈Q, forms a subfield of R

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