Modular Arithmetic

(See attached file for full problem description) --- Seeking a clear path because do not understand this concept of modular arthimentic.

Collection of subsets for equivalence relations

Check over and provide input still need help understanding this relation problem.

Discrete Mathematics

I would like to get a more detailed understanding of my homework. I am not looking for just answers, but more a step-by-step solution. I would like to know how? Prove the given statement: 1) The sum of an integer and it's square is even. 2) The sum of the squares of two odd integers cannot be a perfect square. 3) ...continues

Big O and Catalan number proof

Information is in document.

Undirected & Spanning Trees and Reverse Polish Notation

(See attached file for full problem description)

Proofs by induction

I'm having a hard time comprehending how to write proofs by induction. I'm looking for answers to these problems so that I may have a better understanding of how they are done. --- All problems need to be proved using induction in proofs. 1. Consider n infinitely long straight lines, none of which are parallel and no th ...continues

Prove or disprove that if a and b are rational numbers the a^b (a to the power b ) is also rational

Prove or disprove that if a and b are rational numbers the a^b (a to the power b ) is also rational

Proof - show that if r is an irrational number, there is a unique integer n such that the distance between r and n is less than 1/2.

Show that if r is an irrational number, there is a unique integer n such that the distance between r and n is less than 1/2.

Prove that if n is a positive integer then n is even if and only if 7n+4 is even.

Prove that if n is a positive integer then n is even if and only if 7n+4 is even.

Prove that either 2 * 10^500 + 15 or 2 * 10^500 + 16 is not a perfect square. Is your proof constructive or nonconstructive?

Prove that either 2 * 10^500 + 15 or 2 * 10^500 + 16 is not a perfect square. Is your proof constructive or nonconstructive? Note: ^ is to the power of