Symbolic Logic, part I: Introduction to Basic Concepts

One important area of math is “symbolic logic,” which is also known as “formal logic” or sometimes “Boolean algebra.”
Here’s how it starts.  I’m going to start with a statement:

The car is green.

We are going to call this statement P.  Note that when we say “statement,” we mean something that is factual, not opinion.  So “The car is green” is okay (as long as we agree what “green” is: but, I digress), but “The car is beautiful” is not.  Our statement P can have one of two states: It can either be True or it can be False.  If we were to put these possible values into a table, they would look like this:

P

True

False

It may seem a bit silly to have such a table, but I’m introducing it here to introduce the concept of the “Truth table.” This is the truth table of the statement P.

Note that there is no “Maybe” listed here.  That’s because in logic, a statement is either totally true or it is totally false.  There is no middle ground; the car is either green or it is not.  If it’s “kinda” green, then it’s not green, and the statement would be false.  Now, we could get into arguments about the definition of “green,” and get into specific color wavelengths on the electromagnetic spectrum, but for our purposes, green is green, and a car is either green or it isn’t.

Then there is this statement:

The car is not green.

We could call this statement “not P.”  We would symbolize it thusly: ~P.  Whenever P is True, ~P is false, and vice versa.  The truth table would look like this:

P	~P
True	False
False	True

Next: We will be introducing compound statements.