ECON 1530 Lecture Notes - Lecture 22: Logical Truth, Validity

• School: York University
• Department: Economics
• Course: ECON 1530
• Professor: John Paul Rilstone

Document Summary

Econ 1530 lecture 22 notes mathematical proofs. Introduction: example, find all x such that, solution, squaring both sides of the given equation yields, consequently, that is, from the latter equation it follows that, which yields, or, thus, a necessary condition for x to solve. Inserting these two possible values of x into the original equation shows that only x = 0 satisfies the equation: the unique solution to the equation is, therefore, x = 0. It is important to note, however, that the implication cannot be replaced by equivalence. If a2 = b2, then either a = b or a = b. It need not be true that a = b. In this case, we begin by supposing that q is not true, and on that basis demonstrate that p cannot be true either: this is completely legitimate, because we have the following equivalence: is equivalent to.