ECS 20 Study Guide - Final Guide: Fibonacci Number, Propositional Calculus, Mathematical Induction

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

Document Summary

Part i: logic (2 questions, each 10 points; total 20 points: for each of the five propositions in the table below, indicates on the right if they are always tautologies or not (p and q are propositions). If 2+6 = 5 then 10 = -9 ( p p) q ( p q) p if 3+3 = 6 then 25=16+9 ( p p) ( p p: let us play a logical game. You find yourself in front of three rooms whose doors are closed. You are told that behind one of the doors there is a princess and behind the two other doors there are tigers. The guardian in front of door 1 tells you, The guardian in front of door 3 tells you, Part ii: proofs and number theory (4 questions; each 10 points; total 40 points: let a and b be two strictly positive real numbers. Prove that a b a 2 .