Question

In: Advanced Math

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. Let...

Unless otherwise noted, all sets in this module are finite. Prove the following statements...

1. Let S = {0, 1, . . . , 23} and define f : Z→S by f(k) = r when 24|(k−r). If g : S→S is defined by (a) g(m) = f(7m) then g is injective and (b) g(m) = f(15m) then g is not injective.

2. Let f : A→B and g : B→C be injective. Then g ◦f : A→C is injective.

3. Let f : A→B and g : B→C be surjective. Then g ◦ f : A→C is surjective.

4. There is a surjection f : A→B such that f −1 : B→A is not a function.

Solutions

Expert Solution


Related Solutions

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. If...
Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. If A and B are sets then (a) |A ∪ B| = |A| + |B| − |A ∩ B| and (b) |A × B| = |A||B|. 2. If the function f : A→B is (a) injective then |A| ≤ |B|. (b) surjective then |A| ≥ |B|. 3. For each part below, there is a function f : R→R that is (a) injective and surjective. (b)...
Let A and B be finite sets. Prove the following: (a) |A∪B|=|A|+|B|−|A∩B| (b) |A × B|...
Let A and B be finite sets. Prove the following: (a) |A∪B|=|A|+|B|−|A∩B| (b) |A × B| = |A||B| (c) |{f : A → B}| = |B||A|
Use a 5% significance level for all hypothesis tests (α=.05) unless otherwise noted. Give conclusions as...
Use a 5% significance level for all hypothesis tests (α=.05) unless otherwise noted. Give conclusions as complete sentences. This is considered an ‘open book’ test so you may use the text, StatCrunch, any notes you have, or lecture videos. You should not consult other individuals. 1. A marketing firm was hired by the Acme Company to determine if internet advertising for the company was equally effective in reaching men and women. They sampled 675 men and 703 women and found...
Prove the following statements! 1. If A and B are sets then (a) |A ∪ B|...
Prove the following statements! 1. If A and B are sets then (a) |A ∪ B| = |A| + |B| − |A ∩ B| and (b) |A × B| = |A||B|. 2. If the function f : A→B is (a) injective then |A| ≤ |B|. (b) surjective then |A| ≥ |B|. 3. For each part below, there is a function f : R→R that is (a) injective and surjective. (b) injective but not surjective. (c) surjective but not injective. (d)...
Montevideo Company had the following account balances for the quarter ending March 31, unless otherwise noted:...
Montevideo Company had the following account balances for the quarter ending March 31, unless otherwise noted: Work-in-process inventory (January 1) $ 140,400 Work-in-process inventory (March 31) 171,000 Finished goods inventory (January 1) 540,000 Finished goods inventory (March 31) 510,000 Direct materials used 378,000 Indirect materials used 84,000 Direct manufacturing labor 480,000 Indirect manufacturing labor 186,000 Property taxes on manufacturing plant building 28,800 Salespersons' company vehicle costs 12,000 Depreciation of manufacturing equipment 264,000 Depreciation of office equipment 123,600 Miscellaneous plant overhead...
Assume cash transaction in year X1 unless otherwise noted. 1/1       An Investor acquired 100% of Crazy’s...
Assume cash transaction in year X1 unless otherwise noted. 1/1       An Investor acquired 100% of Crazy’s stock with an investment of $800,000 cash. Par value of stock was 20.00/share and a thousand shares were sold 1/1       Crazy borrowed $250,000 cash by issuing a 3-year note with a stated interest rate of 8% per year. To be compounded annually. The interest will be paid on January 1 of each year (starting next year); and the principal will be paid on...
Assume cash transaction in year X1 unless otherwise noted. 1/1       An Investor acquired 100% of Crazy’s...
Assume cash transaction in year X1 unless otherwise noted. 1/1       An Investor acquired 100% of Crazy’s stock with an investment of $800,000 cash. Par value of stock was 20.00/share and a thousand shares were sold 1/1       Crazy borrowed $250,000 cash by issuing a 3-year note with a stated interest rate of 8% per year. To be compounded annually. The interest will be paid on January 1 of each year (starting next year); and the principal will be paid on...
Assume no arbitrage unless otherwise noted. A stock is currently priced at $39.00. The risk free...
Assume no arbitrage unless otherwise noted. A stock is currently priced at $39.00. The risk free rate is 4.9% per annum with continuous compounding. Every 6 months, its price will either go up by 17% or down by 19%. Consider a European put with strike $42.00 expiring in 12 months. (a) Using the binomial tree model, compute the price of a European put option at the initial node, the two intermediate nodes, and the three terminal nodes. Enter the following...
Use the following information to create the financial statements in questions 1-3. Unless otherwise specified, the...
Use the following information to create the financial statements in questions 1-3. Unless otherwise specified, the data given are for the fiscal year 2019 as of Dec. 31. Credit will not be given unless complete financial statements are submitted. Sales revenue: $8,000 Accounts Receivable Dec. 31, 2019: $150 Tax rate: 25% Accounts Payable Dec. 31, 2019: $175 Interest expense: $70 Inventory Dec. 31, 2019: $800 SGA Expenses: $1,300 Total Expenses: $5,200 Other Revenue: $2,000 Accrued Liabilities: $550 R&D Expense: $500...
5. Prove the Following: a. Let {v1, . . . , vn} be a finite collection...
5. Prove the Following: a. Let {v1, . . . , vn} be a finite collection of vectors in a vector space V and suppose that it is not a linearly independent set. i. Show that one can find a vector w ∈ {v1, . . . , vn} such that w ∈ Span(S) for S := {v1, . . . , vn} \ {w}. Conclude that Span(S) = Span(v1, . . . , vn). ii. Suppose T ⊂ {v1,...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT