MATH135 Study Guide - Contraposition, Coprime Integers, Binary Relation

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Martin Pei

Document Summary

De nition: an impication is a statement s such that a hypothesis (or assumption) h ensures the validity of the conclusion c, and may either be true or false. An implication is only false if a hypothesis is true and the conclusion is false (ie a counter-example exists). In other words, for s: p = q (p implies q), s is true unless p is true and q is false. Note that this can give confusing results such as: if 1 = 2, then 2 = 2, if 1 = 2, then 2 = 3. Because 1 = 2 is a false hypothesis, both of these implications are true, regardless of the vailidty of their conclusion. Proposition: for s0 = a = b, s1 = b = c, and s2 = a = c, prove s2 given s0 and s1. Since both a and a = b are true, b is true.