There's a printable worksheet for this chapter. Click on logic15work.rtf.

Here are some more theorems.

Theorems 5 & 6 (De Morgan's Laws) 3. ~(P ^ Q) (~P v ~Q) 4. ~(P v Q) (~P ^ ~Q) |

If they're not obviously true to you, consider the following little dialog.

Which sentences have the same truth functions? Which truth functions are unique?

Notice that Ma ^ Md and Ma v Md have truth functions that are

Another way to get used to De Morgan's laws is to explore the logical properties of the three operators involved ("^", "V" and "~"). Take the following set of arguments and determine which ones are valid and which are invalid, using truth tables where necessary. (There's a printable worksheet. Click on logic15work.rtf)

When you have thoroughly explored the logic of all these arguments, look at the following list of

If you've correctly identified all the valid and invalid arguments, your pattern of circles and crosses should make deMorgan's laws abundantly clear.

Notice that De Morgan's Laws

Neither are ~(R v S) and ~R v ~S or ~(R ^ S) and ~(R v S).

The only two logical equivalences we have are (~R v ~S) ~(R ^ S) and ~(R v S) (~R ^ ~S)

Notice the following facts about applications of DML to placeholders like "S" and "R"..

1. If we start with

2. If we start with

3. If we start with a

4. If we start with a

5. If we start without parentheses, we end up with them.

6. If we start with parentheses, we end up without them.

Finally, and to practice for the inevitable quiz, go through the following arguments again, this time ignoring the issue of validity, pick out all and only the arguments that represent instances of de Morgan's laws. (Remember,

Now, the following is

I found this representation of de Morgan's Laws at the Museum of Jurassic Technology. What do you think? (More images on Flickr) logic alphabet

http://en.wikipedia.org/wiki/Shea_Zellweger

http://www.logic-alphabet.net/

http://www.valdostamuseum.org/hamsmith/SheaZintro.html

http://www.cabinetmagazine.org/issues/18/crystal.php

http://www.flickr.com/photos/43992178@N00/387339135/

Copyright © 2009 by Martin C. Young

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