Unformatted text preview: ersal generalization the truth of the original formula follows. ༉ So, we must prove something of the form: Reminder: Even and Odd Integers Deﬁnition: The integer n is even if there exists an integer k such that n = 2k, and n is odd if there exists an integer k, such that n = 2k + 1. Note that every integer is either even or odd and no integer is both even and odd. We will need this basic fact about the integers in some of our example proofs. Proving Condi$onal Statements: p → q ༉ a) Trivial Proof: If we know q is true, then p → q the whole statement is true as well. “If it is raining then 1=1.” ༉ b) Vacuous Proof: If we know p is false then p → q the whole statement is true as well. “If I am both rich and poor then 2 + 2 = 5.” Even though these examples seem silly, both trivial and vacuous proofs are often used in mathematical induction. P...
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This document was uploaded on 02/27/2014 for the course CS 215 at SIU Carbondale.
 Spring '14
 M.Nojoumian
 Computer Science

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