Homework Answers
We have constructed the proof by selecting appropriate sentences.
Add Answer to:
UUIDOR Quiz 2 - Ma Consider the following theorem. Theorem: The sum of any even integer...
1 point Prove the following statement: If n2 is even, then n is even. Order each of the following sentences so that the...
1 point Prove the following statement: If n2 is even, then n is even. Order each of the following sentences so that they form a logical proof. Proof by Contrapositive: Choose from these sentences: Your Proof: Suppose n is odd. Then by definitionn 2k +1 for some integer k Required to show if n is not even (odd), then n is not even (odd). Thus n2(2k1)2. n24k2 4k1. 22(22+2k) +1 Thus n2 (an integer) +1 and by definition is odd....
In the following problem, we will work through a proof of an important theorem of arithmetic. Your job will be to read the proof carefully and answer some questions about the argument. Theorem (The Di...
In the following problem, we will work through a proof of an
important theorem of arithmetic. Your job will be to read the proof
carefully and answer some questions about the argument. Theorem
(The Division Algorithm). For any integer n ≥ 0, and for any
positive integer m, there exist integers d and r such that n = dm +
r and 0 ≤ r < m. Proof: (By strong induction on the variable n.)
Let m be an arbitrary...
1. [10 marks] Modular Arithmetic. The Quotient-Remainder theorem states that given any integer n and a positive integer...
1. [10 marks] Modular Arithmetic. The Quotient-Remainder theorem states that given any integer n and a positive integer d there exist unique integers q and r such that n = dq + r and 0 r< d. We define the mod function as follows: (, r r>n = qd+r^0<r< d) Vn,d E Z d0 Z n mod d That is, n mod d is the remainder of n after division by d (a) Translate the following statement into predicate logic:...
please answer questions #7-13 7. Use a direct proof to show every odd integer is the...
please answer questions #7-13
7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
The Fibonacci Sequence F1, F2, ... of integers is defined recursively by F1=F2=1 and Fn=Fn-1+Fn-2 for each integer . Pro...
The Fibonacci Sequence F1, F2, ... of
integers is defined recursively by F1=F2=1
and Fn=Fn-1+Fn-2 for each integer
. Prove
that (picture) Just the top one( not
7.23)
n 3 Chapter 7 Reviewing Proof Techniques 196 an-2 for every integer and an ao, a1, a2,... is a sequence of rational numbers such that ao = n > 2, then for every positive integer n, an- 3F nif n is even 2Fn+1 an = 2 Fn+ 1 if n is odd....
tell me the answer,don't explain Outline a proof of the following statement by writing the "starting...
tell me the answer,don't
explain
Outline a proof of the following statement by writing the "starting point" and the "conclusion to be shown" in a proof of the statement: For all integers a, b, and c, if a b and ac, then a (5b + 3c). That is, complete the sentences below. Proof: Assume We must show that Assume that a(5b + 3c); We must show that alb, and alc. Oa Assume a = 2, b=6, c=12; We must show...
Question 8: For any integer n 20 and any real number x with 0
Question 8: For any integer n 20 and any real number x with 0<<1, define the function (Using the ratio test from calculus, it can be shown that this infinite series converges for any fixed integer n.) Determine a closed form expression for Fo(x). (You may use any result that was proven in class.) Let n 21 be an integer and let r be a real number with 0<< 1. Prove that 'n-1(2), n where 1 denotes the derivative of...
8.5 Theorem. Let s andt be any two different natural numbers with s t. Then (2st. (). is a Pythagorean triple. The prec...
8.5 Theorem. Let s andt be any two different natural numbers with s t. Then (2st. (). is a Pythagorean triple. The preceding theorem lets us easily generale infinitely many Pythagorean triples, but, in fact, cvery primitive Pythagorean triple can be generated by chousing appropriale natural numbers s and and making the Pythagorean triple as described in the preceding thcorem. As a hint to the proof, we make a little observation. 8.6 Lemma. Let (a, b,e) be a primitive Pythagorean...
QUESTION: PROVE THE FOLLOWING 4.3 THEOREM IN THE CASE r=1(no induction required, just use the definition of the determ...
QUESTION: PROVE THE FOLLOWING 4.3 THEOREM IN THE CASE
r=1(no induction required, just use the definition of the
determinants)
Theorem 4.3. The determinant of an n × n matrix is a linear function of each row when the remaining rows are held fixed. That is, for 1 Sr S n, we have ar-1 ar-1 ar-1 ar+1 ar+1 ar+1 an an rt whenever k is a scalar and u, v, and each a are row vectors in F". Proof. The proof...
PROOFS: Use these theorems and others to prove these statements. Theorem 1: The sum of two...
PROOFS: Use these theorems and others to prove these statements. Theorem 1: The sum of two rational numbers is rational. Theorem 2: The product of two rational numbers is rational. Theorem 3: √ 2 is irrational. Induction: Prove that 6 divides n 3 − n for any n ≥ 0 Use strong induction to prove that every positive integer n can be written as the sum of distinct powers of 2. That is, prove that there exists a set of...
1 point Prove the following statement: If n2 is even, then n is even. Order each of the following sentences so that they form a logical proof. Proof by Contrapositive: Choose from these sentences: Your Proof: Suppose n is odd. Then by definitionn 2k +1 for some integer k Required to show if n is not even (odd), then n is not even (odd). Thus n2(2k1)2. n24k2 4k1. 22(22+2k) +1 Thus n2 (an integer) +1 and by definition is odd....
In the following problem, we will work through a proof of an
important theorem of arithmetic. Your job will be to read the proof
carefully and answer some questions about the argument. Theorem
(The Division Algorithm). For any integer n ≥ 0, and for any
positive integer m, there exist integers d and r such that n = dm +
r and 0 ≤ r < m. Proof: (By strong induction on the variable n.)
Let m be an arbitrary...
1. [10 marks] Modular Arithmetic. The Quotient-Remainder theorem states that given any integer n and a positive integer d there exist unique integers q and r such that n = dq + r and 0 r< d. We define the mod function as follows: (, r r>n = qd+r^0<r< d) Vn,d E Z d0 Z n mod d That is, n mod d is the remainder of n after division by d (a) Translate the following statement into predicate logic:...
please answer questions #7-13
7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
The Fibonacci Sequence F1, F2, ... of
integers is defined recursively by F1=F2=1
and Fn=Fn-1+Fn-2 for each integer
. Prove
that (picture) Just the top one( not
7.23)
n 3 Chapter 7 Reviewing Proof Techniques 196 an-2 for every integer and an ao, a1, a2,... is a sequence of rational numbers such that ao = n > 2, then for every positive integer n, an- 3F nif n is even 2Fn+1 an = 2 Fn+ 1 if n is odd....
tell me the answer,don't
explain
Outline a proof of the following statement by writing the "starting point" and the "conclusion to be shown" in a proof of the statement: For all integers a, b, and c, if a b and ac, then a (5b + 3c). That is, complete the sentences below. Proof: Assume We must show that Assume that a(5b + 3c); We must show that alb, and alc. Oa Assume a = 2, b=6, c=12; We must show...
Question 8: For any integer n 20 and any real number x with 0<<1, define the function (Using the ratio test from calculus, it can be shown that this infinite series converges for any fixed integer n.) Determine a closed form expression for Fo(x). (You may use any result that was proven in class.) Let n 21 be an integer and let r be a real number with 0<< 1. Prove that 'n-1(2), n where 1 denotes the derivative of...
8.5 Theorem. Let s andt be any two different natural numbers with s t. Then (2st. (). is a Pythagorean triple. The preceding theorem lets us easily generale infinitely many Pythagorean triples, but, in fact, cvery primitive Pythagorean triple can be generated by chousing appropriale natural numbers s and and making the Pythagorean triple as described in the preceding thcorem. As a hint to the proof, we make a little observation. 8.6 Lemma. Let (a, b,e) be a primitive Pythagorean...
QUESTION: PROVE THE FOLLOWING 4.3 THEOREM IN THE CASE
r=1(no induction required, just use the definition of the
determinants)
Theorem 4.3. The determinant of an n × n matrix is a linear function of each row when the remaining rows are held fixed. That is, for 1 Sr S n, we have ar-1 ar-1 ar-1 ar+1 ar+1 ar+1 an an rt whenever k is a scalar and u, v, and each a are row vectors in F". Proof. The proof...
Most questions answered within 3 hours.
-
1.How large must the coefficient of static friction be between
the tires and the road if...
asked 8 minutes ago -
What is the time complexity (Big-O) of the following code?
class Main
{
// Recursive...
asked 8 minutes ago -
Economists look at any situation in terms of its component
parts: the people making decisions, the...
asked 13 minutes ago -
What is a population?
Select one:
a. All of the individual organisms belonging to the same...
asked 18 minutes ago -
You have a yeast cell culture with a concentration of 5x10^4
cells/ml. If you dilute this...
asked 22 minutes ago -
In which direction the Reaction goes? Show detailed process.
SeO3 + 2ClO2. + 2H3O <---> Se...
asked 35 minutes ago -
Unexposed silver halides are removed from photographic film when
they react with sodium thiosulfate
(Na2S2O3, called...
asked 36 minutes ago -
A 0.3054 gram sample of the mineral chalcopyrite (CuFeS2)
yielded 0.6525 gram BaSO4 precipitate. What is...
asked 36 minutes ago -
An short-seller in Tesla is worried the latest management
earnings forecast is too aggressive and the...
asked 1 hour ago -
Question 3 (1 point)
Fill in the blank. Speed Car Rental company found that the tire...
asked 1 hour ago -
1. A copper wire is 26.61 cm long and weighs 1.265 g. The
density of copper...
asked 59 minutes ago -
Remember that a concept sketch consists of a sketch (or
series of sketches), labels, and complete...
asked 1 hour ago