﻿CS 201 - 12/1/14 Exam 1 Count: 30 Max: 98 Min: 14 Ave: 54 Median: 51 90's 1 80's 4 70's 2 60's 6 50's 2 40's 7 30's 5 20's 1 10's 2 ====================================== ChiQat Lab - Class on Date: 12/02/2014 (Tuesday next week) - Lab Location- SCE 408 - Time Start: 11:00 AM - Time End: 12:15 PM --------------------------------------- a. All healthy people eat an apple a day. b. Herbert is not a healthy person. c. ∴ Herbert does not eat an apple a day. h(X) X is a healthy person a(X) X eats an apple a day H is Herbert h(H) Herbert is a healthy person a(H) Herbert eats an apple a day a. (ForAll X) h(X)->a(X) b. ~h(H) or NOT(h(H)) c. :. ~a(H) by Rule of Universal Modus Ponens (ForAll X) p(X)->q(X) p(A) :. q(A) The above argument does NOT match Universal Modus Ponens by Rule of Universal Modus Tollens (ForAll X) p(X)->q(X) ~q(A) :. ~p(A) The above argument does NOT match Universal Modus Tollens The above argument is NOT valid ------------ for the statement: if p then q (p -> q) the converse is: if q then p (q -> p) the converse cannot be counted as always being true. when we have: p -> q q :. p We have an invalid argument using the converse error the inverse is: if ~p then ~q (~p -> ~q) the inverse cannot be counted as always being true when we have: p -> q ~p :. ~q We have an invalid argument using the inverse error ---------------- For the argument of: a. (ForAll X) h(X)->a(X) b. ~h(H) c. :. ~a(H) This is an invalid argument using the inverse error