Question

Write a formal proof to prove the following conjecture to be true or false. If the...

Write a formal proof to prove the following conjecture to be true or false.

If the statement is true, write a formal proof of it. If the statement is false, provide a counterexample and a slightly modified statement that is true and write a formal proof of your new statement.

Conjecture: There does not exist a pair of integers m and n such that m^2 - 4n = 2.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Determine if each of the following statements is true or false. If a statement is true,...
Determine if each of the following statements is true or false. If a statement is true, then write a formal proof of that statement, and if it is false, then provide a counterexample that shows its false. 1) For each integer a there exists an integer n such that a divides (8n +7) and a divides (4n+1), then a divides 5. 2)For each integer n if n is odd, then 8 divides (n4+4n2+11).
1. For each statement that is true, give a proof and for each false statement, give...
1. For each statement that is true, give a proof and for each false statement, give a counterexample     (a) For all natural numbers n, n2 +n + 17 is prime.     (b) p Þ q and ~ p Þ ~ q are NOT logically equivalent.     (c) For every real number x ³ 1, x2£ x3.     (d) No rational number x satisfies x^4+ 1/x -(x+1)^(1/2)=0.     (e) There do not exist irrational numbers x and y such that...
Write a formal proof where you define a function to prove that the sets 3Z and...
Write a formal proof where you define a function to prove that the sets 3Z and 6Z have the same cardinality, meaning |3 Z| = |6 Z|. 3Z = {..., −3, 0, 3, 6, 9, ...} and 6Z = {..., −6, 0, 6, 12, 18, ...} Z = integers
For each of the following statements: if the statement is true, then give a proof; if...
For each of the following statements: if the statement is true, then give a proof; if the statement is false, then write out the negation and prove that. For all sets A;B and C, if B n A = C n A, then B = C.
4. Let f be a function with domain R. Is each of the following claims true...
4. Let f be a function with domain R. Is each of the following claims true or false? If it is false, show it with a counterexample. If it is true, prove it directly from the FORMAL DEFINITION of a limit. (a) IF limx→∞ f(x) = ∞ THEN limx→∞ sin (f(x))  does not exist. (b) IF f(−1) = 0 and f(1) = 2 THEN limx→∞ f(sin(x)) does not exist.
1. Write a proof for all non-zero integers x and y, if there exist integers n...
1. Write a proof for all non-zero integers x and y, if there exist integers n and m such that xn + ym = 1, then gcd(x, y) = 1. 2. Write a proof for all non-zero integers x and y, gcd(x, y) = 1 if and only if gcd(x, y2) = 1.
Prove or disprove the following statements. Remember to disprove a statement you have to show that...
Prove or disprove the following statements. Remember to disprove a statement you have to show that the statement is false. Equivalently, you can prove that the negation of the statement is true. Clearly state it, if a statement is True or False. In your proof, you can use ”obvious facts” and simple theorems that we have proved previously in lecture. (a) For all real numbers x and y, “if x and y are irrational, then x+y is irrational”. (b) For...
Discrete math problem! Prove or disprove the following statement: “If two rectangles have the same area...
Discrete math problem! Prove or disprove the following statement: “If two rectangles have the same area and the same perimeter, then they have the same dimensions (length, width).” Note that finding a pair of rectangles that meet the criteria and showing that their dimensions are the same is an example, not a proof. If you feel that the statement is false, then demonstrate it by showing that it leads to a contradiction, or by finding a counterexample.
(a) Is the converse of Bolzano-Weierstrass Theorem true? If yes prove it. If false provide a...
(a) Is the converse of Bolzano-Weierstrass Theorem true? If yes prove it. If false provide a counterexample. (b) Since Q is countably infinite, it can be written as a sequence {xn}. Can {xn} be monotone? Briefly explain. Hint. Assume it’s monotone, what would be the consequences? (c) Use the , N definition to prove that if {xn} and {yn} are Cauchy then {xn + yn} is Cauchy too.
Is the following statement true? "If f (Y − X) = f (Y ) − f...
Is the following statement true? "If f (Y − X) = f (Y ) − f (X) for all sets X and Y with X ⊆ Y ⊆ A, then f : A → B is injective." Please provide a proof if it is true, and a counterexample if it is false.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT