The diagram below shows a directed graph: http://imgur.com/a/fxqVD (a) Is <d, b, c, g, c, f, e, c, d> a circuit in the graph? Is it a cycle? (b) What is the longest cycle in the...

The diagram below shows a directed graph: http://imgur.com/a/fxqVD (a) Is <d, b, c, g, c, f, e, c, d> a circuit in the graph? Is it a cycle? (b) What is the longest cycle in the...

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

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

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

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 6 officers be chosen if the President and atleast one other officer must be at least...

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.

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...

For a 2 coin toss experiment, what are the set of events that are statistically independent when you assume: a) equally likely outcomes b) not equally likely outcomes c) What...

For a 2 coin toss experiment, what are the set of events that are statistically independent when you assume: a) equally likely outcomes b) not equally likely outcomes

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! its a combinations question. Thank you!

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

Pleas help! Not sure how to do this

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...

how many elements are in the set {(x,y)∈ AxA|x+y is even} if A={1,2,3,4,5}. Please explain all steps. Thank You!!

Given the information x1=1 and x2=2, and ∀ n≥2, xn+1=4xn-5xn-1, find explicitly the values of p,q which make xn=p(2+i)n+q(2+i)n for every n. I am really having...

let n∈N. if a,b,c,d ∈ N and a≡b (mod n) and c≡d (mod n) prove that ac≡bd (mod n). Please, any help would be greatly appreciated. This is a study question on my study guide and I'm having...

prove that there does not exist n∈N such that n≡2 (mod 4) and n≡4 (mod 8). Please help this was on my last exam but I was very lost and my professor did not have enough time to go over it in class...

I would really appreciate any help you can give me. I'm struggling a lot with this problem. Thank you!!