Question

Prove that there is no positive integer n so that 25 < n2 < 36. Prove...

Prove that there is no positive integer n so that 25 < n2 < 36. Prove this by directly proving the negation. Your proof must only use integers, inequalities and elementary logic. You may use that inequalities are preserved by adding a number on both sides, or by multiplying both sides by a positive number. You cannot use the square root function. Do not write a proof by contradiction.

Homework Answers

Answer #1

Please feel free to ask any doubts regarding the solution and please rate positively.

Kind regards.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that there is no positive integer n so that 25 < n^2 < 36. Prove...
Prove that there is no positive integer n so that 25 < n^2 < 36. Prove this by directly proving the negation.Your proof must only use integers, inequalities and elementary logic. You may use that inequalities are preserved by adding a number on both sides,or by multiplying both sides by a positive number. You cannot use the square root function. Do not write a proof by contradiction.
Let n be an integer. Prove that if n is a perfect square (see below for...
Let n be an integer. Prove that if n is a perfect square (see below for the definition) then n + 2 is not a perfect square. (Use contradiction) Definition : An integer n is a perfect square if there is an integer b such that a = b 2 . Example of perfect squares are : 1 = (1)2 , 4 = 22 , 9 = 32 , 16, · · Use Contradiction proof method
Prove the following theorem: For every integer n, there is an even integer k such that...
Prove the following theorem: For every integer n, there is an even integer k such that n ≤ k+1 < n + 2. Your proof must be succinct and cannot contain more than 60 words, with equations or inequalities counting as one word. Type your proof into the answer box. If you need to use the less than or equal symbol, you can type it as <= or ≤, but the proof can be completed without it.
Prove the following theorem: For every integer n, there is an even integer k such that...
Prove the following theorem: For every integer n, there is an even integer k such that n ≤ k+1 < n + 2. Your proof must be succinct and cannot contain more than 60 words, with equations or inequalities counting as one word. Type your proof into the answer box. If you need to use the less than or equal symbol, you can type it as <= or ≤, but the proof can be completed without it.
Discrete Math 6. Prove that for all positive integer n, there exists an even positive integer...
Discrete Math 6. Prove that for all positive integer n, there exists an even positive integer k such that n < k + 3 ≤ n + 2 . (You can use that facts without proof that even plus even is even or/and even plus odd is odd.)
Prove that a positive integer n, n > 1, is a perfect square if and only...
Prove that a positive integer n, n > 1, is a perfect square if and only if when we write n = P1e1P2e2... Prer with each Pi prime and p1 < ... < pr, every exponent ei is even. (Hint: use the Fundamental Theorem of Arithmetic!)
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square...
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square root of 17 is irrational too, for any natural number n. use the following lemma: Let p be a prime number; if p | a2 then p | a as well. Indicate in your proof the step(s) for which you invoke this lemma. Check for yourself (but you don’t have to include it in your worked solutions) that this need not be true if...
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square...
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square root of 17 is irrational too, for any natural number n. use the following lemma: Let p be a prime number; if p | a2 then p | a as well. Indicate in your proof the step(s) for which you invoke this lemma. Check for yourself (but you don’t have to include it in your worked solutions) that this need not be true if...
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...
Suppose that Y has a gamma distribution with α = n/2 for some positive integer n...
Suppose that Y has a gamma distribution with α = n/2 for some positive integer n and β equal to some specified value. Use the method of moment-generating functions to show that W = 2Y/β has a χ2 distribution with n degrees of freedom. (Please show all work, proof used, and logic to justify the answer. Thank, you)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT