detailed solution

E. Prove the following using the indicated method. 1. Prove using direct proof that Vb E N, s.t. 1 s b $ 10, b2 - b + 11 is a prime number. 2. Prove that V2 is irrational by contradiction. if x is even 3. Prove using any methods that Z3 XA , if x is odd 4. Let S(n) = >lo ar' where r # 1 and n 2 0. Show by Principle of Mathematical Induction that S(n) - a(1-r+ 1-7