Give a counterexample to show that the given transformation is not a linear transformation. T[x y] = [y x^2] T[x y] = [|x| |y|] T[x y] = [xy x+y] T[x y] = [x+1 y-1].
give a recursive definition of
a) the set of odd positive integers
b) the set of positive integer powers of 3
c) the set of polynomials with integer coefficients.
Give clear English translations of the following sentences of FOL. Which of the following are logically equivalent and which are not? Explain your answers. THERE EXISTS!xTove(x) [Remember that the notation THERE EXISTS is an abbreviation, as explained above.] THERE EXISTSx FOR ALLy [Tove(y) rightarrow y = x] THERE EXISTSxFOR ALLy.
Give a function in which g(x,y) can have a critical point where the gradient of g does NOT = 0.
Please also include a possible critical point.
g(x,y) = ? Critical point at ( ? , ? ).
Give an example of an arbitrarily large finite abelian group G in which the discrete logarithm problem can be solved efficiently. Ie. For which there exists an algorithm to solve the discrete log problem in G whose run time is a polynomial function in ln(|G|). Justify..
Give a counterexample to A - B = B - A. Give an example where .A - B = B - A. Set difference is not an associative operation either. Give a counterexample to A - (B - C) = (A - B) - C..
give an example of two functions y = f(x) and y = g(x) such that
as the limit approaches 0 f(x) = 0 and as lim approaches 0 f(x) g(x) = 1
Please answer neatly! Thanks!.
Give full solutions to get all the credit
A local credit union has investments in three states-Massachusetts, Nebraska, and California. The deposits in each state are divided between consumer loans and bonds. The amount of money (in thousands of dollars) invested in each category is displayed in.
Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is a constant for sufficiently small n. Make your bounds as tight as possible and fully justify your answers. a) T(n) = T(n 3) + n2 .
b) T(n) =.
Give an infinite set which has greater cardinality than infinitely many different infinite sets which each have different cardinality than each other..
Give a formula for the function illustrated using a vertical shift of an exponential function. The two points marked on the graph are A=(1,30) and B=(1,0). The red horizontal line is given by y=2, and is a horizontal asymptote of the function.
A.
Give a nontrivial example of an infinite dimensional vector space that contains a finite dimensional subspace (your subspace can’t just be the zero vector). Be sure to prove that the subspace is a subspace and has finite dimension..
Give an example of a 3 x 3 matrix whose column space is a plane through the origin in R^3. What kind of geometric object is the nullspace of your matrix? Explain your answer. What kind of geometric object is the row space of your matrix? Explain your answer..
Give an example of denumerable sets A and B, neither of which is a subset of the other, such that
a. AB is denumerable.
b. AB is finite.
c. A-B is denumerable.
d. A-B is finite and nonempty..
Give a context-free grammars that generate the following languages. Assume sigma = {0, 1}. {w | w contains at least three 1's} {w | w starts and ends with the same symbol}.
Give an example of a group with the indicated combination of properties an infinite cyclic group an infinite Abelian group that is not cyclic a finite cyclic group with exactly six generators a finite Abelian group that is not cyclic.
Give an example of integers a and b such that a divides b2, but a does not divide b. Let b Z. Prove that if p is a prime number that divides b2, then p divides b. (Say what fact or theorem you are using.) Suppose a, b, and p.
Give an example of two sequences (x_n) and (y_n) and a partial limit x of (x_n) and a partial limit of y of (y_n) such that x + y fails to be a partial limit of the sequence (x_n + y_n)..
Give an example of a polynomial function that has only imaginary zeros and a polynomial function that has only real zeros. Explain how to determine graphically if a function has only imaginary zeros.
Explain, using a rational function, which function, x2 or x1.5 approaches infinity more quickly..
Give an example of four different subsets A, B, C, and D of {1,2,3,4} such that all intersections of two subsets are different.
I thought I understood this one but keep getting it wrong. Thanks for any help!.
