Discrete Math : Set Relations

Let SIGMA = {a,b} be an alphabet. a. List between braces the elemnts of SIGMA4. the set of strings of length over SIGMA. b. Let A = SIGMA1 U SIGMA2 and B = SIGMA3 U SIGMA4. Describe A, B and AUB in plain English.

Discrete Math

The following is is meant to have some assumptions made (like "n"). I have been up all night trying to figure this out. It can't be Euler because the vertices can't be >1. It might be Hamilton if I assume that E of G(V,E) is infinte..but how would I get my answer? I would just have sets (e1, e2,...) Could this be a straight directed graph where I just count my vertices? If I substitute n for say...4, then I would have 4 vertices? therefore, 4 light are needed to be ordered? (sounds too simple) Please help guide me in the right direction! 1. A contractor for a Paradise city on the XYZ planet has to order traffic lights for the city. All streets in the city are straight a... click for more

Discrete Math

Please help me with this one! 1. Let G be an undirected graph with n vertices. If G is isomorphic to its own compliment , how many edges must G have?

Discrete structures

.Derive the statement as corollaries of other theorems from the text or of statement you have proved true in the exercise. Prove that if one solution to a quadratic equation of the form x^2+bx+c=0 is rational (where b and c are rational), then the other solutions is also rational. (Use the fact that if the solutions of the equation are r & s, then x^2+bx+c=(x-r)(x-s).)

Disprove the statement by giving a counterexample

For all real number a & b, if a