Homework Answers
This question deals with basic properties of sets.
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(a) If E1, E2, En are sets, show rI b) Show that the empty set is a subset of every set c) Show t...
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...
If A and B are sets and f : A → B, then for any subset...
If A and B are sets and f : A → B, then for any subset S of A we define f(S) {be B : b-f(a) for some a ε S). Similarly, for any subset T of B we define the pre-image of T as Note that f (T) is well defined even if f does not have an inverse! Now let fRR be defined as f(x) 2. Let Si denote the closed interval [-2,1], that is all TE R...
ILULIITUL 10.37 Theorem. (The Generalized Distributive Laws for Sets of Sets.) Let S be a set...
ILULIITUL 10.37 Theorem. (The Generalized Distributive Laws for Sets of Sets.) Let S be a set and let be a non-empty set of sets. Then: (a) SNU =USNA: AE}. (b) Sund= {SUA:AE). Proof (a) Let = {SNA: AE }. We wish to show that S U = UB. For each 1, we have BESUS iff x S and 2 EU iff xe S and there exists AE such that EA iff there exists AE such that reS and x E...
Real Analysis II Please do it without using Heine-Borel's theorem and do it only if you're sure Problem: Let E be a closed bounded subset of En and r be any function mapping E to (0,∞). Then t...
Real Analysis II
Please do it without using Heine-Borel's theorem
and do it only if you're sure
Problem: Let E be a closed bounded subset of
En and r be any function mapping E to
(0,∞). Then there exists finitely many points yi ∈ E, i
= 1,...,N such that
Here Br(yi)(yi) is the open ball
(neighborhood) of radius r(yi) centered at
yi.
Also, following definitions & theorems should help
that
E CUBy Definition. A subset S of a topological...
The attached document is a C++ source code, INTERFACE__Class{aSet}.cpp, which contains an interface for class aSet and an implementation section which is largely left empty, so that students could fill in the missing code, where it is written // C++ code
/* FILE NAME: Class{aSet}.cpp FUNCTION: A template class for a set in C++. It implements all the set operations, except set compliment: For any two sets, S1 and S2 and an element, e A. Operations which result in a new set: (1) S1 + S2 is the union of S1 and S2 (2) S1 - S2 is the set difference of S1 and S2, S1 - S2 (3) S1 * S2 is the set intersection of S1 and S2, S1 * S2 (4) S1 + e (or e +...
17-26 true or false questions 17. The smallest positive real number is c, where c = card(0,1). 18. To show that two sets A and B are equal, show that x A and x B. 19. If (vx)P(e) is false, then P...
17-26
true or false questions
17. The smallest positive real number is c, where c = card(0,1). 18. To show that two sets A and B are equal, show that x A and x B. 19. If (vx)P(e) is false, then P(x) is never true for that domain. 20. If R is a relation on A and if (a, a) is true for some a in A, then R is reflexive. 21. If f:A → B is a function, then...
Please help me solve 3,4,5 3- For all n € N, let an = 1. Let...
Please help me solve 3,4,5
3- For all n € N, let an = 1. Let S = {an in€ N}. 3-1) Use the fact that lim - = 0 and the result of Exercise 1 to show that 0 ES'. Ron 3-2) Use the result of Exercise 2 to show that S = {0}. 4- Prove that 4-1) N' = 0. 4-2) Q =R. 5- Recall that a set KCR is said to be compact if every open cover...
Please do exercise 129: Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N...
Please do exercise 129:
Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N → N be the unique function that satisfies f(0) = 2 and f(next(n)) =r(f(n)) for all n E N. 102 1. Prove that f(3) = 8. 2. Prove that 2 <f(n) for all n E N. Exercise 129: Define r and f as in Exercise 128. Assume that x + y. Define r' = {(x,y),(y,x)}. Let g:N + {x,y} be the unique function that...
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that t...
Please all thank you
Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
ARE MY ANSWERS CORRECT? 25 questions 1. what an A/R aging analysis is, its purpose, and...
ARE MY ANSWERS CORRECT? 25 questions 1. what an A/R aging analysis is, its purpose, and how it is created. Used to estimate amount needed in Allowance for Bad Debts Account (a contra account) A/R Days Outstanding 0-30 31-60 61-90 Over 90 Under each term list all A/Rs that are not paid by date Use historical experience to estimate the percentage of A/R for each date period to determine allowance for Bad Debts What the three major cost components are...
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...
If A and B are sets and f : A → B, then for any subset S of A we define f(S) {be B : b-f(a) for some a ε S). Similarly, for any subset T of B we define the pre-image of T as Note that f (T) is well defined even if f does not have an inverse! Now let fRR be defined as f(x) 2. Let Si denote the closed interval [-2,1], that is all TE R...
ILULIITUL 10.37 Theorem. (The Generalized Distributive Laws for Sets of Sets.) Let S be a set and let be a non-empty set of sets. Then: (a) SNU =USNA: AE}. (b) Sund= {SUA:AE). Proof (a) Let = {SNA: AE }. We wish to show that S U = UB. For each 1, we have BESUS iff x S and 2 EU iff xe S and there exists AE such that EA iff there exists AE such that reS and x E...
Real Analysis II
Please do it without using Heine-Borel's theorem
and do it only if you're sure
Problem: Let E be a closed bounded subset of
En and r be any function mapping E to
(0,∞). Then there exists finitely many points yi ∈ E, i
= 1,...,N such that
Here Br(yi)(yi) is the open ball
(neighborhood) of radius r(yi) centered at
yi.
Also, following definitions & theorems should help
that
E CUBy Definition. A subset S of a topological...
17-26
true or false questions
17. The smallest positive real number is c, where c = card(0,1). 18. To show that two sets A and B are equal, show that x A and x B. 19. If (vx)P(e) is false, then P(x) is never true for that domain. 20. If R is a relation on A and if (a, a) is true for some a in A, then R is reflexive. 21. If f:A → B is a function, then...
Please help me solve 3,4,5
3- For all n € N, let an = 1. Let S = {an in€ N}. 3-1) Use the fact that lim - = 0 and the result of Exercise 1 to show that 0 ES'. Ron 3-2) Use the result of Exercise 2 to show that S = {0}. 4- Prove that 4-1) N' = 0. 4-2) Q =R. 5- Recall that a set KCR is said to be compact if every open cover...
Please do exercise 129:
Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N → N be the unique function that satisfies f(0) = 2 and f(next(n)) =r(f(n)) for all n E N. 102 1. Prove that f(3) = 8. 2. Prove that 2 <f(n) for all n E N. Exercise 129: Define r and f as in Exercise 128. Assume that x + y. Define r' = {(x,y),(y,x)}. Let g:N + {x,y} be the unique function that...
Please all thank you
Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
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