As I was writing the third article in this discrete series, I noticed in the last article I had failed to mention an integral piece of basic discrete. That being, statements and statment symbols. This will be relatively short, but nonetheless important.

Terms

Conditional Operation (p→qp \to q): Read as “if p, then q”.

ppqqp→qp \to q
111
100
011
001

If you’re like me, then this table may seem confusing. To get a better idea of it, think of it as a promise:

“If you clean your room (p), you get ice cream (q).”

  • This promise is only False (or broken) when you clean your room (p = 1 [or true]), but don’t get ice cream (q = 0 [or false]).
  • If you don’t clean your room but still get ice cream, the promise wasn’t broken (it never forbade getting ice cream other ways).
  • If you don’t clean your room and don’t get ice cream, the promise was still not broken. In logic, if the promise isn’t broken, the statement is considered True (1). broken.