{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Examples 7.3 - Examples 7.3 Rules of Replacement The first...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Examples 7.3 Rules of Replacement! The first 8 rules were technically rules of inference . That is, given a few premises (maybe only one), you could infer some other particular premise (or conclusion). Here the idea is that you can replace a premise with something else (that’s logically equivalent). Also, critically, you can replace parts of lines according to these rules . Here are the first 5 of them. [The ratings are to be considered as a combination of frequency of use AND the sneakiness of their usage . The frequency of their use is supposed to determine the urgency with which I would press you to remember them. That is, if the rule will be used a lot, you had better know it. The sneakiness factor is supposed to indicate how hard it will be to see when to use the rule, though using it will be vital for deriving the conclusion.] DeMorgan’s Rule (DM) ~(p · q) :: (~p v ~q) ~(p v q) :: (~p · ~q) I’m not going to bother with any justification for these types of replacement—it’s too complicated to be useful (in a way that I think, like, Conjunction is not). If you’re really in doubt, compose a truth table and compare the statements. You’ll see that they have the same TVs under the main operator. What does that mean?? That’s right; they’re logically equivalent. (Note: the ‘::’ means just ‘is logically equivalent to’; it means you can replace one side with the other, if you need—it’s not strictly left to right, or vice versa) This rule is rather important.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}