21127 Lecture Notes - Lecture 13: Universal Quantification, Logical Biconditional, Contraposition
16 Dec 2015
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Document Summary
Always distinguish between what we want to show and what we currently know. Keep track on the side of your goal and your assumptions, and ll in the gaps. I like to think of the what we currently know as a bag of tricks. The bag changes over the course of a proof, and is di erent from proof to proof, but the goal of any proof is to add the desired conclusion, what we want to show, to our bag of tricks. Speci cally, consider the following table that summarizes when we should let a variable be arbitrary and. Xed versus when we should de ne/choose a variable. It depends on whether we know or want to show (wts) a quanti ed statement, and what quanti er that is. Check out the proof strategies sheet i posted on the website for more info about this! Let a and b be any two sets.
