Let f be ac on [a,b]. Show that the total variation Va() is ac on [a,b].
Let A and B be two sets. (a) Show that Ac = (Ac ∩ B) ∪ (Ac ∩ Bc ), Bc = (A ∩ Bc ) ∪ (Ac ∩ Bc ). (b) Show that (A ∩ B) c = (Ac ∩ B) ∪ (Ac ∩ Bc ) ∪ (A ∩ Bc ). (c) Consider rolling a fair six-sided die. Let A be the set of outcomes where the roll is an odd number. Let B be the set of outcomes...
A. (Leftovers from the Proof of the Pigeonhole Principle). As before, let A and B be finite sets with A! 〉 BI 〉 0 and let f : A → B be any function Given a A. let C-A-Va) and let D-B-{ f(a)} PaRT A1. Define g: C -> D by f(x)-g(x). Briefly, if g is not injective, then explain why f is not injective either. Let j : B → { 1, 2, 3, . . . , BI}...
20.1. Show that if f : [a, b R is of bounded variation, then it is integrable on [a, b]. ; (bi: i)(DULO(ld rl. VZLilin.l.ld DILL.
20.1. Show that if f : [a, b R is of bounded variation, then it is integrable on [a, b]. ; (bi: i)(DULO(ld rl. VZLilin.l.ld DILL.
Let R(A,B,C,D) be a relation with FDs F = {A—B, AC, C-A, B,C, ABC-D} Which of the following statements is correct ? (2 points) Select one: G = {A-B, B-C, C-A, AC=D } is a canonical cover of F H = { AC, CA, BC,BD} is a canonical cover of F. o F is a canonical cover of itself. O G and H are canonical covers of F. None of the above.
Finding Measures of variation. In Exercises find the (a) explained variation (b) unexplained variation, (c) total variation, (d) coefficient of determination, and (e) standard error of estimate se. In each case, there is a significant linear correlation so that it is reasonable to use the regression equation when making predictions.Cholesterol and BMI Refer to the paired cholesterol/BMI data for women as listed in Data Set 1 in Appendix B. (Let x represent the cholesterol levels.)
(4) Let F be a field and let a, b E F with a 0. Show that Fx/axb)F
(4) Let F be a field and let a, b E F with a 0. Show that Fx/axb)F
Bonus Let F: NW be liniar at Va,V EV, LFügt >=<a, FJ> df a, b + 0,274, Fra)=2a , F(b) = ut, then what is true of Tech, a) att bl <a h> 50 c) (2-4) <a,b> >0 ) (24) La, b><o
Let A. B, C, D є Mnxn(F), and det(A) 0, AC-CA. Prove that A B det ( )) -det(AD CB)
b and c please explian thx
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post the question from the book
Let 2 be a non-empty set. Let Fo be the collection of all subsets such that either A or AC is finite. (a) Show that Fo is a field. Define for E e Fo the set function P by ¡f E is finite, 0, if E is finite 1, if Ec is finite. P(h-10, (b) If is countably infinite, show P is finitely additive but not-additive. (c)...
7. Let S : X Y and B CY. Show that f[f-?[B]] CB and = B if f is surjective. 8. Show that the set of infinite sequences from 0, 1 is not countable. (Hint: Let : N → E. Then f(m) is a sequence < amn>0. Let bm = 1 - amm. Then <b > is a sequence in E and for each k, <br>< akn >= f(k). This is "Cantor's diagonal process".]