Symbolic Logic 3: The Or Operator

In the last post, we discussed the “And” operator (symbolized as “∧” as in “P ∧ Q”).  Today, we’re going to discuss its brother, “Or.”
Similar to the And operator, Or is symbolized thusly:

P∨Q

And just like And, an Or statement can be evaluated to True or False.  The difference with Or is that it evaluates to False only if both component statements are False.  Here is the truth table for P∨Q

P	Q	P ∨ Q
True	True	True
True	False	True
False	True	True
False	False	False

The definition of the “Or” operator could be this:

The “Or” operator evaluates to False if and only if both component operands are False.

If you’ll recall, we had values for P and Q:

P=”The car is green”
Q=”The car has four doors.”

So P ∨ Q would read as:

Either the car is green or it has four doors, or both.

If our hypothetical car has two doors, this statement is still true, because both predicates must evaluate to False in order for the whole thing to be False.  In fact, let’s look at the truth table for this statement, just for fun:

Either the car is green or it doesn’t have four doors, or both.

That would be symbolized like this:

P ∨ ~Q

Here’s the truth table of that statement:

P	Q	~Q	P∨~Q
True	True	False	True
True	False	True	True
False	True	False	False
False	False	True	True

This is interesting.  This statement seems to be false only if it has four doors, but it isn’t green.  Might there be a causal relationship here?  Let’s look at this another way.  Let’s say P=”The car is a coupe.” and Q=”The car is fast.”  P ∨ ~Q seems to imply that in order for you to have a fast car, it must be a coupe.  That seems to say something wholly different.  I’ll cover that in my next post.
Next: Differentials
Next in the Logic Series: The If… Then Operator