Tuesday, June 14, 2011

De Morgan's Laws

I spent most of the morning creating a forum post asking for people's  opinions of Chris Hecker's physics references list.  I posted it on four  forums: The Bullet Physics Simulation Forum, GameDev.net, TIGSource, and Physics Forums.   It's been interesting to see how active the various forums are.  Bullet  and Physics Forums are about equal at 32 views and 33 views with 0  replies.  GameDev.net appears to be the least active at 0 views and 0  replies, although I suspect that this may have something to do with  differences in the counting systems used.  TIGSource is definitely the  most active at 181 views and 12 replies.

When I had time to study math, I finished off the section on sets.  I  learned what a universal set is (the set which all the currently  discussed sets are subsets of), as well as what the complement of a set  is (it is the set of all elements in the universal set except the  elements belonging to the set being operated on). I also learned about  De Morgan's laws in relation to set theory, including how to prove  them.  The first law states that the complement of the union of two sets  A and B is equal to the intersection of the complements of the two sets  A and B.  The second law states that the complement of the intersection  of two sets A and B is equal to the union of the complements of the two  sets A and B.  One of the problems in the problem set was proving De  Morgan's second law.  It took me about an hour to figure out, but I  eventually proved it by doing a lot of substitution and logic.

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