ECS 20 Study Guide - Final Guide: Mathematical Induction, Unit Circle, 3I
12 Oct 2018
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I will grade however over a total of 60, i. e. one question can be considered extra credit . Part i: logic (3 questions, each 5 points; total 15 points: on a distant island, every inhabitant is either a knight or knave. You meet three inhabitants: a, b and: a says, c is not a knave . B says, c and a are both knights . C says, a is a knight or b is a knave . ] r p q: show that the proposition, let us play a logical game. You find yourself in front of three rooms whose doors are closed. The three numbers (n-1)3, n3 and (n+1)3 are three consecutive perfect cubes. (hint: start by showing that for all integer n) Id:______ __________________________: n is a positive integer. Prove that 12 | (n2-1) if gcd(n,6) = 1 (hint: write n=6k+l, and show that if gcd(n,6)=1, then l = 1 or l = 5).
