CPSC 121 Study Guide - Midterm Guide: Vacuous Truth, Without Loss Of Generality, Sequential Logic

• School: UBC
• Department: Computer Science
• Course: CPSC 121
• Professor: All

Document Summary

[wlog], or direct proof [antecedent assumption]) that makes as much progress as possible on the proof. Note that you do not have enough information to actually prove the theorem! For the second, slightly altered statement, explain why the statement will probably be easy to prove or disprove. Suggest an approach for: x d, p (x) q(x) Solution : one plausible approach is to use a direct proof: we consider an unspec- i ed element x of the domain, we assume that p (x) holds, and then we show that. Q(x) holds using only p (x) and properties that are true for every element of d (that is, we can not assume anything speci c about the value of x or its properties). Explain why this will be easy to prove/disprove: x d, p (x) q(x) Solution : this theorem is true if there is at least one element x of d for which p (x) is false.