Prove that √3 is irrational using contradiction. You can use problem 4 as a lemma for...

Prove that √3 is irrational using contradiction. You can use problem 4 as a lemma for this.

Problem 4, for context is

Prove that if n² is divisible by 3, then n is divisible by 3.

Expert Solution

Colby Messinger answered 2 years ago

4. Use a proof by contradiction to show that the square root of 3 is irrational....

4. Use a proof by contradiction to show that the square root of 3 is irrational. You may use the following fact: For any integer k, if k2 is a multiple of 3, then k is a multiple of 3. Hint: The proof is very similar to the proof that √2 is irrational. 5. Use a direct proof to show that the product of a rational number and an integer must be a rational number. 6. Use a proof by...

Prove by contradiction, every real solution of x3+x+3=0 is irrational.

Do not use Pumping Lemma for Regular Expression to prove the following. You may think of...

Do not use Pumping Lemma for Regular Expression to prove the following. You may think of Closure Properties of Regular Languages 1. Fix an alphabet. For any string w with |w| ≥ 2, let middle(w) be the string obtained by removing the first and last symbols of w. That is, Given L, a regular language on Σ, prove that f1(L) is regular, where f1(L) = {w : middle(w) ∈ L}

Problem 4 ..... you can use Matlab Using the same initial code fragment as in Problem...

Problem 4 ..... you can use Matlab Using the same initial code fragment as in Problem 1, add code that calculates and plays y (n)=h(n)?x (n) where h(n) is the impulse response of an IIR bandstop filter with band edge frequencies 750 Hz and 850 Hz and based on a 4th order Butterworth prototype. Name your program p3.sce the below is the Problem 1 initail code .. you can use it Matlab The following cilab code generates a 10-second “chirp”...

Prove that {anbamba2m+n:n,m≥1} is not regular using pumping lemma

Use the pumping lemma to prove that the following languages are not regular. (a)L2 = {y...

Use the pumping lemma to prove that the following languages are not regular. (a)L2 = {y = 10 × x | x and y are binary integers with no leading 0s, and y is two times x}. (The alphabet for this languages is {0, 1, ×, =}.) For example, 1010 = 10 × 101 is in L2, but 1010 = 10 × 1 is not. (b)Let Σ2 = {[ 0 0 ] , [ 0 1 ] , [ 1...

Prove that the set of irrational numbers is uncountable by using the Nested Intervals Property.

prove that the set of irrational numbers is uncountable by using the Nested Intervals Property

Using the pumping lemma, prove that the language {1^n | n is a prime number} is...

Using the pumping lemma, prove that the language {1^n | n is a prime number} is not regular.

(35 pt.) Prove that the following languages are not regular using the pumping lemma. (15pt.)?={?????? |?,?≥?}...

(35 pt.) Prove that the following languages are not regular using the pumping lemma. (15pt.)?={?????? |?,?≥?} (20 pt.) ? = {? ∈ {?, #}∗ | ? = ??#??# ... #?? ??? ? ≥ ?, ?? ∈ ?∗ ??? ????? ?, ??? ?? ≠?? ???????? ?≠?} Hint: choose a string ? ∈ ? that contains ? #’s.

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