suppose that in solving a tsp you use the cheapest link algorithm and find a cheapest link tour with a length of 21400 miles. suppose that you later find out that the length of an optimal tour is...

suppose that in solving a tsp you use the cheapest link algorithm and find a cheapest link tour with a length of 21400 miles. suppose that you later find out that the length of an optimal tour is...

Determine is, in general, true or false. Recall that a universal statement is true if it is true for all possible cases while it is false if there is even one counterexample. Be prepared to...

prove that for every n∈N , ( 2n choose n) is even

use the well-ordering principle. Please help with this question, it's a practice problem, I just can't figure out. Thank you!

let m,n belong to N, and m,n>1, prove that mn< (m+n)choose 2 Please help. Thank you!

let 〈xn〉n=1...∞ be a sequence satisfying xn+1=xn-xn-1 for each n. Prove that ∀ n ∈ N, xn+6=xn by induction Please help me. I'm reviewing for my final and something...

let 〈xn〉n=1...∞ be a sequence satisfying xn+1=xn-xn-1 for each n. Prove that ∀ n ∈ N, xn+6=xn by induction

let G=(V,E) be a graph where V={A⊆N5||A|=2} and E={{A,B}⊆V|A∩B=ø} sketch this graph and find its size

Please help! I do not know how to do this practice problem. My professor told us to try it for fun. But, he never went over it in class. And now im curious

A club has 30 members under the age of 30 and 40 members who are 30 or older. In how many ways can a slate of officers be chosen if the President and atleast one other officer must be at least 30...

please help, Im very confused. This one on my exam and I didnt understand it at all. Want to know the answer so I can study for my final.

Ten people check their hats in a resturant. The resturant is evacuated quickly. Everyone grabs a hat. In how many ways can it happen, that noone gets the right hat? Please...

(Proof by contradiction the following statement) If a and b are rational numbers, b does not = 0, and r is an irrational number, then a + br is irrational.

let〈an〉∞n=1 and 〈bn〉∞ n=1 by sequences of numbers Then ∀ m∈N ∑(an+bn) = (∑an) +(∑bn) Proof by induction Side note:...

Please help! its a combinations question. Thank you!

Any help would be greatly appreciated. Thanks!

Suppose A is a set and B is a set. Given that |AυB|=50;|A`B|=20 and |B`A|=15, find |A| and |B| "`" is the closest symbole I could find for set subtraction. PLEASE...

Prove by induction that every n∈N, (1+√3)n+(1-√3)∈Z. I have an exam tonight and this was one of the practice problems I do not understand. PLEASE HELP! Thank you

Suppose a,b,x,y are integers and that p is a prime. Show that if ax + by = p, then gcd(a,b) = 1 or gcd(a,b) = p.

Let a,b, and c be integers such that c doesn't equal 0. Show that if gcd(a,c) = 1 and c divides ab, then c divides (cx + by) for all x,y Hint. use euclid's Lemma

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