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 three of which have a common point of intersection. Show that for n >= 1, the lines divide the plane into (n^2 + n + 2)/2 separate regions. 2. A string of 0s and 1s is to be processed and converted to an even-parity string by adding a parity bit to the end of the string. The parity bit is initially 0. When a 0 character is processed, the parity bit remains unchang... click for more

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