MA121 Lecture Notes - Lecture 3: Contraposition, List Of Theorems, Mathematical Induction
Document Summary
Review summary for the tutorial and written quizzes of lab 3. The most commonly seen expressions in mathematical theorems are implication statements in the logial form. P q (read if p , then q ). Implication statements may be proved using one of the following methods. If 5n 9 is odd, then n is even: direct proof. This method of proof is a valid argument consisting of explicit or implicit premises and the conclusion q. The statement p must appear as a premise. other explicit premise(s) (such as the de nition(s) involved) other implicit premise(s) (such as known theorem(s) that can be applied) A typical, fatal mistake in using this method is to actually apply (or just simply assume) the conclusion q as a premise in the proof: proving its contrapositive. Because the conditional p q is equivalent to its contrapositive q p, we can prove the statement q p instead and then claim the original statment is also true.
