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1. Given a family A,...An of sets (not necessarily disjoint), a trunsversal is a set T such that ...
(a) If E1, E2, En are sets, show rI b) Show that the empty set is a subset of every set c) Show t...
need some with these. thanks
(a) If E1, E2, En are sets, show rI b) Show that the empty set is a subset of every set c) Show that EnE (d) Show that if E is any event of a sample space S, then E UE -S (e) Show that i E CF, ten F EU(En F). Also show the sets E and En F are disjoint. (1) Show for any two sets, E and F, we have F-(EnF)U(EnF). Also...
1. (Set theory review.) Let A and B be sets, and let F be a family...
1. (Set theory review.) Let A and B be sets, and let F be a family of sets. Give a logical statement equivalent to each of the following. Your answer should only use the E symbol, basic logical symbols (E, V, A, V, 7, +, ++), variable names, and parentheses. • ACB. • A and B are disjoint. • XEAN B. • XENF.
A set function, λ on S by λ((a, b) F(b)--F(a) and λ(0) 1. Show that if Eİ, E2 E S then Ei n E2 ES...
a set function, λ on S by λ((a, b) F(b)--F(a) and λ(0) 1. Show that if Eİ, E2 E S then Ei n E2 ES and Ei ~ E2 is a finite disjoint union of 0. sets in S 2. Show that the o-algebra generated by S is the Borel o-algebra on R. 3. Show that if E and Ea are disjoint sets in S and A U S, then (A) A(E)+A(B2). 4, Show that if E. .. ova natn...
Sets, Please respond ASAP, Thank you 2) Recall another notation for the natural numbers, N, is...
Sets,
Please respond ASAP,
Thank you
2)
Recall another notation for the natural numbers, N, is Z+. We similarly define the negative integers by: 2. Too, for any set A and a e R, define: and Let B={x: x E Z+ & x is odd } (Recall a number I is said to be odd if 2k +1 for some k e z) Assume Z is our underlying background set for this problem. (a) Write an expression for 3 +...
6) Which of the following is a possible set of quantum numbers for a 4f electron? (n, t, me, m) A) 4,2, 1,- B) 3,4,...
6) Which of the following is a possible set of quantum numbers for a 4f electron? (n, t, me, m) A) 4,2, 1,- B) 3,4, 3,+ C) 4,3, 3,+ D) 4, 2, 2,+½ E) 4, 3,-4,-½ 7) 7) Choose the ground state electron configuration for Cr. A) [Ar]4s 3d B) [Ar]4s 3d C) [Ar]4s 3d D) [Ar] E) [Ar]3d 8) 8) Calculate the wavelength, in nanometers, of an x-ray that has frequency of 5.15 x 10 s A) 1.72x 10...
1. Let U be the universal set with disjoint subsets A and B, where n(U-46, n(A-15,...
1. Let U be the universal set with disjoint subsets A and B, where n(U-46, n(A-15, and n(B-14. Find nAn B 2. A merchant surveyed 300 people to determine the way they leaned about an upcoming sale. The survey showed that 180 learned about the sale from the radio, 170 from television, 130 from the newspaper, 120 from radio and television, 70 from radio and newspapers, 80 from television and newspapers, and 60 from all three sources. How many people...
4. Let T be a linear operator on the finite-dimensional space V with eharacteristie polynomial and minimal polynomial Let W be the null space of (T c) Elementary Canonical Forms Chap. 6 226 (a)...
4. Let T be a linear operator on the finite-dimensional space V with eharacteristie polynomial and minimal polynomial Let W be the null space of (T c) Elementary Canonical Forms Chap. 6 226 (a) Prove that W, is the set of all vector8 α in V such that (T-cd)"a-0 for some positive integer 'n (which may depend upon α). (b) Prove that the dimension of W, is di. (Hint: If T, is the operator induced on Wi by T, then...
7. Consider a set of particles in a ring in flat space-time. The coordinates of any...
7. Consider a set of particles in a ring in flat space-time. The coordinates of any particle in the ring is given by x, y or equivalently by r, where I = r cos 0 and y=rsin. During the passage of a gravitational wave the proper distance between the origin (t=y=0) and any particle in the ring is given by: As = R [1+34, cos(wt) cos(20) (9) a) Show that if we change to a coordinate system X, Y where...
1. Problem 1. Given a data set (X, Y), use the least squares techniques to find the best ftting c...
1. Problem 1. Given a data set (X, Y), use the least squares techniques to find the best ftting curve y-/() within the exponential family v ab) where a,b ER. The data set is given by, where, χ-io, 0.2, 0.4, 0.6, 08, 09, 1, 12, 14, 1.6] y 2, 2.5, 3.1, 3.9, 4.8, 5.4, 6, 7.5, 9.3, 11.6] In particular: a) Going from the original data (x,Y) set to the transformed data set (X, Z) with z(Y)-In (Y), verify that...
need some with these. thanks
(a) If E1, E2, En are sets, show rI b) Show that the empty set is a subset of every set c) Show that EnE (d) Show that if E is any event of a sample space S, then E UE -S (e) Show that i E CF, ten F EU(En F). Also show the sets E and En F are disjoint. (1) Show for any two sets, E and F, we have F-(EnF)U(EnF). Also...
1. (Set theory review.) Let A and B be sets, and let F be a family of sets. Give a logical statement equivalent to each of the following. Your answer should only use the E symbol, basic logical symbols (E, V, A, V, 7, +, ++), variable names, and parentheses. • ACB. • A and B are disjoint. • XEAN B. • XENF.
a set function, λ on S by λ((a, b) F(b)--F(a) and λ(0) 1. Show that if Eİ, E2 E S then Ei n E2 ES and Ei ~ E2 is a finite disjoint union of 0. sets in S 2. Show that the o-algebra generated by S is the Borel o-algebra on R. 3. Show that if E and Ea are disjoint sets in S and A U S, then (A) A(E)+A(B2). 4, Show that if E. .. ova natn...
Sets,
Please respond ASAP,
Thank you
2)
Recall another notation for the natural numbers, N, is Z+. We similarly define the negative integers by: 2. Too, for any set A and a e R, define: and Let B={x: x E Z+ & x is odd } (Recall a number I is said to be odd if 2k +1 for some k e z) Assume Z is our underlying background set for this problem. (a) Write an expression for 3 +...
6) Which of the following is a possible set of quantum numbers for a 4f electron? (n, t, me, m) A) 4,2, 1,- B) 3,4, 3,+ C) 4,3, 3,+ D) 4, 2, 2,+½ E) 4, 3,-4,-½ 7) 7) Choose the ground state electron configuration for Cr. A) [Ar]4s 3d B) [Ar]4s 3d C) [Ar]4s 3d D) [Ar] E) [Ar]3d 8) 8) Calculate the wavelength, in nanometers, of an x-ray that has frequency of 5.15 x 10 s A) 1.72x 10...
1. Let U be the universal set with disjoint subsets A and B, where n(U-46, n(A-15, and n(B-14. Find nAn B 2. A merchant surveyed 300 people to determine the way they leaned about an upcoming sale. The survey showed that 180 learned about the sale from the radio, 170 from television, 130 from the newspaper, 120 from radio and television, 70 from radio and newspapers, 80 from television and newspapers, and 60 from all three sources. How many people...
4. Let T be a linear operator on the finite-dimensional space V with eharacteristie polynomial and minimal polynomial Let W be the null space of (T c) Elementary Canonical Forms Chap. 6 226 (a) Prove that W, is the set of all vector8 α in V such that (T-cd)"a-0 for some positive integer 'n (which may depend upon α). (b) Prove that the dimension of W, is di. (Hint: If T, is the operator induced on Wi by T, then...
7. Consider a set of particles in a ring in flat space-time. The coordinates of any particle in the ring is given by x, y or equivalently by r, where I = r cos 0 and y=rsin. During the passage of a gravitational wave the proper distance between the origin (t=y=0) and any particle in the ring is given by: As = R [1+34, cos(wt) cos(20) (9) a) Show that if we change to a coordinate system X, Y where...
1. Problem 1. Given a data set (X, Y), use the least squares techniques to find the best ftting curve y-/() within the exponential family v ab) where a,b ER. The data set is given by, where, χ-io, 0.2, 0.4, 0.6, 08, 09, 1, 12, 14, 1.6] y 2, 2.5, 3.1, 3.9, 4.8, 5.4, 6, 7.5, 9.3, 11.6] In particular: a) Going from the original data (x,Y) set to the transformed data set (X, Z) with z(Y)-In (Y), verify that...
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