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Suppose that n is a positive integer and that n = ab, where
Suppose that n is a positive integer and that n = ab, where a and b are relatively prime positive integers. Define a function f: Un → Ua × Ub by f([x]) = ([x], [x]). Prove that f is surjective.Start b… read more
NicoletaB45
NicoletaB45
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Question 3 tests your understanding of set notation, and your
Question 3 tests your understanding of set notation, and your ability to prove that one set is a proper subset of another. Consider the following subsets of R2: A = {(x, y) ∈ R2 : x2 + y2 ≤ 9}, B = {(… read more
Stevewh
Stevewh
Teacher
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Define the function f : N → N as follows. f(n) =<: f(n) =1
Define the function f : N → N as follows. f(n) =<: f(n) =1 if n = 1 f(n) =5 if n = 2 f(n) =f(n − 1) + 2f(n − 2) if n ≥ 3 Prove that f(n) = 2n + (−1)n for all integers n ≥ 1.… read more
Dr Arthur Rubin
Dr Arthur Rubin
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Doctoral Degree
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Define the function f : N → N as follows. f(n) =<: f(n) =1
Define the function f : N → N as follows. f(n) =<: f(n) =1 if n = 1 f(n) =5 if n = 2 f(n) =f(n − 1) + 2f(n − 2) if n ≥ 3 Prove that f(n) = 2n + (−1)n for all integers n ≥ 1.… read more
Osbert12
Osbert12
Master's Degree
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I have some multiple choice questions I need help with, due
I have some multiple choice questions I need help with, due within the next hour. Can you help?… read more
Dr. Dan
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Doctoral Degree
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The equation x^2n+y^2n+z^2n 1, where n is a positive integer,
The equation x^2n+y^2n+z^2n=1, where n is a positive integer, describes a flattened sphere. Define the extreme points to be the points on the flattened sphere with a maximum distance from the origin. … read more
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Dr. Dan
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I want to make sure that I am doing something the right way
I want to make sure that I am doing something the right way for the below Discrete Math problem: The President assured the American people that "In all my years of public service, I have never obstruc… read more
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Dr. Dan
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(4) Let P(x) be the sentence the word x contains the letter
(4) Let P(x) be the sentence “ the word x contains the letter ‘a' or ‘c' but not both”. What are the truth values of the following? (a) 1. P(faulty) (b) 2. P(sensible)] (c) 3. P(cardboard)] (d) 4. P(c… read more
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Dan
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1.The following algorithm adds all entries in a square n *
1.The following algorithm adds all entries in a square n * n array A. Analyze this algorithm where the work unit is the addition operation Sum =0 For i=1 to n do For j=1 to n do Sum = sum + A[I,j] End… read more
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Dan
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2 For every positive odd integer n Prove that n^2 2n + 3
2 For every positive odd integer n Prove that n^2 = 2n + 3 for n = 3 5 A string of 0s and 1s is to be processed and converted to an even –parity string by adding a parity bit to the end of the string.… read more
Dan
Dan
Doctoral Degree
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I have a few number theory questions. 1) Suppose that m is
I have a few number theory questions. 1) Suppose that m is a number such that phi(m) divides m-1. Show that there does not exist a prime such that p^2 divides m. 2) Show that phi(2n) = the piecewise f… read more
Dan
Dan
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1. Prove that the acute angle whose cosine is 3/7 cannot be
1. Prove that the acute angle whose cosine is 3/7 cannot be trisected with straightedge and compass. 2. Find the cardinality of the set of all lines in the plane. Prove that your answer is correct. 3.… read more
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Dr. Dan
Doctoral Degree
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1. Use mathematical induction to prove that the statements
1. Use mathematical induction to prove that the statements are true for every positive integer n. A. 2 + 4 + 6 +…….. + 2n=n(n+1) B. 5 + 10 + 15 +…….. + 5n = 5n(n+1) -------- 2 2 For every positive odd… read more
Dr. Dan
Dr. Dan
Doctoral Degree
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1. Use the definition of the integral to prove that the function
1. Use the definition of the integral to prove that the function f defined by f(x)=1/x for x does not equal zero and f(0)=0 is not Riemann Integrable on [0,1]. 2. Prove that the function g:[0,1]->R… read more
Jim C
Jim C
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Let f R- R be a monotone and let D be the set of all points
Let f:R->R be a monotone and let D be the set of all points in R at which f is not continuous. Prove D is a countable set. Define functions f and g by f(x)={0, if x0 g(x)={((-1)^n)/(2^n), if x=1/n … read more
Jim C
Jim C
Master's Degree
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1. Use the definition of Uniform Continuity to prove each statement a.
1. Use the definition of Uniform Continuity to prove each statement: a. h(x)= 4/(x^2) is uniformly continuous on [1,5) b. G(x)= x^3 is not uniformly continuous on [0,infinity) c. H(x) = x sin x is not… read more
Jim C
Jim C
Master's Degree
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1.Let a, b, c and d be any real numbers such that a b, c d.
1.Let a, b, c and d be any real numbers such that a… read more
Ben Brown
Ben Brown
Bachelor's Degree
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We say that f R- R is additive if for all x, y E R, f(x+y)
We say that f: R->R is additive if for all x, y E R, f(x+y) = f(x)+f(y). In what follows, f is an additive function. 1. Show that for each positive integer n and each real number x, f(nx)=n(x). &n … read more
Dr Arthur Rubin
Dr Arthur Rubin
Doctoral Degree
Doctoral Degree
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