CSC165H1 Study Guide - Natural Number

• School: UTSG
• Department: Computer Science
• Course: CSC165H1
• Professor: Nathalie Fournier

Document Summary

Summer 2012 (a) x n, y n, yx = y. Then, y n, yx(cid:48) = y # universal introduction. Then, yx(cid:48) = 1y = y # math. Then, x n, y n, yx = y # existential introduction (b) x n, y n, 4y = x. In order to disprove the statement, we need to prove the negation. Then, y(cid:48) n # since x n. Then, 4y(cid:48) = 4x (cid:54)= x # math; x > 0, since we assumed n start with 1. Then, x n, y n, 4y (cid:54)= x # universal introduction. Note: the above proof uses the assumption that natural numbers do not include 0. In the future, we will be using the de nitions of natural numbers which do include 0. This does not change the value of the statement. The proof, however, would be a bit longer.