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I'm going over my Discrete Structures assignment and an operator or something is used that I've never seen in the book or the notes. The questions is- Describe the following sets using the explicit method, withand then it gives sets A B C D and E explicitly, the questions im stuck on is - (C ? E) ? (A -(D ? B)) and B is complemented and D ? B is also complemented... what is that question mark, and what do I do with it??Code:U = {x|x E N ^ 1<x<10}
I don't remember much from my Discrete Math class, but I found this:
Quote:
A group of three people, each of which is a liar (lies all the time) or is a truar (tells the truth all the time) are talking. B says that C and D are the same type (both liars or both truars). Someone then asks D, ``Are B and C the same type?'' What does D answer?
Here's our solution. Let b stand for "B" is a truar", and similarly for c and d. The statement ``C and D are the same type'' is formalized as c == d. Since B said it, we have b == (c == d). D's answer can be formalized as b ? c, where ? is either == if D answers ``yes'' or /== if D answers ``no'', and we have to determine which it is. Since D answers, we write this as d == (b ? c).
We manipulate d == b ? c under the truth of b == c == d. In the manipulation,we omit all parentheses because == is associative and == and /== are mutually associative.
d == b ? c --Fact
= < Fact b == c == d >
b == c == b ? c
By inference rule Equanimity, the last line is a theorem. But the last line is a theorem only if ? is ==. Therefore, we conclude that D answered ``yes''.
actually the GA just emailed me back saying that there aren't any ? in the assignment and then I figured out that because im using OOo it read the word file wrong, too bad he emailed me back after the assignment was due.