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1. Consider functions f : X → Y and g : Y → Z. (a) Suppose that f is surjective. Is g ? f surjective? Either prove it is, or give a counterexample. (b) Suppose that g is surjective. Is g ? f surjective? Either prove it is, or give a counterexample. (c) Suppose that both f and g are surjective. Is g ? f surjective? Either prove it is, or give a counterexample. (d) Suppose that g ? f is surjective. Is g surjective? Either prove it is, or give a counterexample. (e) Suppose that g ? f is surjective. Is f surjective? Either prove it is, or give a counterexample. 2. Let f : X → Y be a function. (a) Let A and B be subsets of X. Define the set A B. (b) Prove that f[A] f[B] ⊆ f[A B]. (c) Now suppose that f : X → Y is injective. Prove that f[A B] ⊆ f[A] f[B]. (d) Give an example of a function f : X → Y together with sets A, B ⊆ X such that f[A B] 6= f[A] f[B].
An executive invests $28,000, some at 6% and some at 5% annual interest. If he receives an annual return of $1540, how much is invested at each rate.
Is there sufficient evidence to indicate premature battery failure at the α = .05 level?
Assume Emerson Electrics managers expect an earnings downturn and a resulting decreases in growth of 3 percent. How does this affect your answers to parts 1 and 2?
a game warden catches, tags and then releases 15 zebras. a month later, a sample of 20 zebras is collected and 6 of them have tags. use this information to estimate the size of the zebra population in that area.
Suppose you just received a shipment of SIX televisions. THREE of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one does not work?
The derivative of a continuous function at x is the slope of the tangent line to the curve at x. The attached pdf file develops the idea of a derivative first using slopes of secant lines and then introducing and explaining the difference quotient..
A closed rectangular box has a volume of 32 cubic centimeters. What are the lengths of the edges giving the minimum surface area?
Test for population mean
An open-topped cylindrical pot is to have volume 125in^3. What dimensions will minimize the total amount of material used in making this pot?
The name of a variable in the C programming language is a string that can contain uppercase letters, lowercase letters, digits, or underscores. Further, the first character in the string must be a letter, either uppercase or lowercase, or an under..
The profits from the product group were further categorized as shown in the second pie chart. How much was the profit from wholesale?
What is the acceleration needed to travel the maximum distance when starting from a standstill? How is acceleration impacted by the distance error?
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