Lemma 1 Total Circlyde Positive Circlyde Size Least 2 Must Pear Adjacent Elements 1 Mod N Q37045139

Lemma 1: If the the total of a circlyde is positive, andthe circlyde has size at least 2, then there must be a pear ofadjacent elements a(i) and a(i+1) mod n whose sum is positive suchthat ai is positive.  

PLEASE ANSWER ALL 4

1. Prove the Circlyde Pair Lemma using an proof technique youwish

Now, we will prove the Fundamental Theorem of Circlydesusing induction on the circlyde

2. State and Prove the Base Case

3.

OR

 

OR