ECS 20 Study Guide - Final Guide: Mathematical Induction, Prime Number, Set Theory

• School: UC-Davis
• Department: Engineering: Computer Science
• Course: ECS 20
• Professor: All

Document Summary

Part i: proofs (4 questions; each 10 points; total 40 points: let a and b be two real numbers with a 0 b 0. Use a proof by contradiction to show a + b. 2 ab . that: let x and y be two integers. Show that if x2+y2 is even, then x+y is even. Id:______ __________________________: let a = {1,2,3} and r = {(2,3),(2,1)} be two sets. Note that in the definition of r, order matters: for example, (2,3) r but (3,2) r . Proof by induction (4 questions; each 10 points; total 40 points) 2n for all integer n 1: show by induction that. Id:______ __________________________: let {an} be a sequence with first terms a1=2, a2=8, and recursive definition: an = 2an 1 +3an 2 +4 . Show that an = 3n 1 for all integer n 1 using strong induction: let x be a positive real number (x>0).